Executive Solution Overview
[>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) Please see attached **files (3)** – ## MATH110WK678DiscussionHelp.docx – ## UsingtheEquationEditorinMyClassroom.pdf – ## AdvancedFunctionsQuestionsandAnswers1.pdf **## MATH110WK678DiscussionHelp.docx** **WK6 Practice wit…
Instant Solution Download
$6.99Immediate access to the full model answer, formatted citations, and rubric breakdown.
Need a Fresh Custom Paper?
Have this question answered from scratch according to your specific instructions and deadline.
Order on TutorsGallery →Assignment Prompt & Instructions
[>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)
Please see attached
**files (3)**
– ## MATH110WK678DiscussionHelp.docx
– ## UsingtheEquationEditorinMyClassroom.pdf
– ## AdvancedFunctionsQuestionsandAnswers1.pdf
**## MATH110WK678DiscussionHelp.docx**
**WK6 Practice with advanced functions**
This discussion may require you to use exponents (superscripts) or log bases (subscripts). A short-cut that is handy for this is that both the superscript key (to make exponents) and the subscript key are in the drop-down menu next to the
U for underline.
For other mathematical symbols, follow the instructions for Using the Equation Editor.
Pick ONE of the problems from this collection "Advanced Functions Questions" that has not already been solved. Pretend that you are tutoring someone who has never seen these problems before and give a detailed demonstration of its solution.
**Note:** Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
Select Start a New Conversation and make the problem number the subject of your post. The answers are provided so don't just give an answer—we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order
to get credit. I will indicate in the grading comments if corrections need to be made. If you haven't received credit, first double-check for my grading comments. If everything looks OK, then email me asking me to check on it.
If I indicate that there is a problem, you must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses to other classmates are required** – your initial post is worth the full points.
**WK7 Conics are Everywhere!**
This week we will investigate conic shapes in the real world.
Begin by selecting Start a New Conversation. Research ONE example of a conic section in real life that has not already been used by a classmate.
Make your choice (Bouncing ball) the subject of your post, and then tell us in your own words about your find. Do not just make this up off the top of your head. The St Louis Arch, for example, is NOT a parabola—it is an inverted catenary.
To get credit for this Discussion, you
**must cite a source** confirming that your example is, indeed, a conic and not some other more exotic curve.
Using a personal example (My eyebrow) will not count unless you can cite a source verifying that eyebrows are parabolic.
You must also respond to 2 classmates' posts. You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another post or share an example from your own life related to the topic.
**WK8 Final Debriefing**
Now that it's the last week of the course, stop by this discussion and tell us what your take was on MATH110 and what your future educational plans are.
Select Start a New Conversation and start a new discussion thread using your name as the subject and then share your thoughts with us.
In terms of this class, you're the expert—what was hard, what was easy, what changes would improve things? Your comments can help us make this a better class for future generations!
In terms of the future – what's next? What classes are you taking in the upcoming semester? Have you decided on a major? How close are you to tossing that mortarboard skyward?
Please also respond to 2 classmates. This is a good time to chime in with advice if you have experience with a class that someone else is about to begin! Just remember to be constructive with comments on an open Discussion!
**## UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## AdvancedFunctionsQuestionsandAnswers1.pdf**
Advanced Functions
1) Solve: 4096x = 8 1)
2) Solve: 1
9
x
= 729 2)
3) Solve: 4
7
x
= 2401
256
3)
4) Solve: 4-x = 1
256
4)
5) Solve: 4(8 – 2x) = 256 5)
6) Solve: 3(6 – 3x) = 1
27
6)
7) Solve: 3(6 + 3x) = 1
27
7)
8) Solve: 4 = b2/3 8)
9) Solve: a3/4 = 125 9)
10) Solve: 25
9
x+1
= 3
5
x-1
10)
11) Solve: e4x – 1 = (e3)-x 11)
12) Solve: 8x – 1 = 323x 12)
13) Solve: m-4 = 1
81
13)
14) Solve: 1
3
2x + 3
= 9x- 5 14)
1
15) Solve: ( 5 )x + 1 = 25x 15)
16) Solve: ex – 3 = 1
e6
x + 2
16)
17) The growth in the mouse population at a certain county dump can be
modeled by the exponential function A(t)= 906e0.012t, where t is the
number of months since the population was first recorded. Estimate the
population after 36 months.
17)
18) The decay of 938 mg of an isotope is given by A(t)= 938e-0.022t, where t
is time in years since the initial amount of 938 mg was present. Find the
amount (to the nearest milligram) left after 96 years.
18)
19) The sales of a mature product (one which has passed its peak) will
decline according to the function S(t) = S0e-at, where t is time in years
since the peak sales. Find the sales of a product 17 years after its peak
sales if a = 0.22 and S0 = 77,500.
19)
20) The number of reports of a certain virus has increased exponentially
since year 0. The number of cases can be approximated using the
function r(t) = 119 e0.008t, where t is the number of years since year 0.
Estimate the number of cases in year 40.
20)
21) An element decays at the rate of S(t) = se-0.048t, where s is the initial
amount in grams and t is the time in years since this initial amount was
present. If you have a 71-gram piece of this element, how many grams
will you have 5 years from now? Round your answer to the nearest
tenth of a gram.
21)
22) Solve: log5 125 = x 22)
23) Solve: log3 1
27
= x 23)
24) Solve: log7 712 = x 24)
25) Solve: logx 625 = 4 25)
2
26) Solve: x = 8log8 13 26)
27) Solve: x = log10 0.01 27)
28) Solve: x = log2
5
8 28)
29) Solve: logx 9 = – 2 29)
30) Solve: log4 x = 3 30)
31) Solve: log5 x = -3 31)
32) Solve: log(x – 5) 10 = 1 32)
33) Solve: log(x + 7) 11 = 1 33)
34) Solve: 8x – 32 = logx 1 34)
35) Suppose f(x) = logax and f(4) = 2. Find f(16). 35)
36) Suppose f(x) = logax and f(4) = 2. Find f 1
16
. 36)
37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 37)
38) Suppose f(x) = loga(x) and f(5) = 2. Find f 5
5
38)
39) Evaluate: 100log107 39)
40) Evaluate: log10(0.01)9 40)
41) Evaluate: 1000log1010 41)
42) Evaluate: log10(0.0001)10 42)
3
43) The growth in population of a city can be seen using the formula p(t) =
2148e0.008t, where t is the number of years. Use this formula to
calculate the population after 10 years.
43)
44) Suppose the government wants to impose a tax on fossil fuels to reduce
carbon emissions. The cost benefit is modeled by
ln(1 – P) = -0.0039 – 0.0051x, where x represents the dollars of tax per ton
of carbon emitted and P represents the percent reduction in emissions of
carbon. (P is in decimal form.) Determine P when x = 63. Round to three
decimal places.
44)
45) Suppose f(x) = 32.6 + 1.2log (x + 1) models salinity of ocean water to
depths of 1000 meters at a certain latitude. x is the depth in meters and
f(x) is in grams of salt per kilogram of seawater. Approximate the
salinity (to the nearest hundredth) when the depth is 771 meters.
45)
4
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
1) 1
4
2) {-3}
3) {-4}
4) {4}
5) {2}
6) {3}
7) {-3}
8) {-8, 8}
9) {625}
10) – 1
3
11) 1
7
12) – 1
4
13) {-3, 3}
14) 7
4
15) 1
3
16) – 9
7
17) 1396
18) 113
19) 1841 units
20) 164 cases
21) 55.9 g
22) {3}
23) {-3}
24) {6}
25) {5}
26) {13}
27) {-2}
28) 3
5
29) 1
3
30) {64}
5
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
31) 1
125
32) {15}
33) {4}
34) {4}
35) 4
36) -4
37) 6
38) -1
39) 49
40) -18
41) 1000
42) -40
43) 2327
44) 0.278
45) 36.07 g/kg
6
– Advanced Functions Questions
– Advanced Functions Answers
**## AdvancedFunctionsQuestionsandAnswers1.pdf**
Advanced Functions
1) Solve: 4096x = 8 1)
2) Solve: 1
9
x
= 729 2)
3) Solve: 4
7
x
= 2401
256
3)
4) Solve: 4-x = 1
256
4)
5) Solve: 4(8 – 2x) = 256 5)
6) Solve: 3(6 – 3x) = 1
27
6)
7) Solve: 3(6 + 3x) = 1
27
7)
8) Solve: 4 = b2/3 8)
9) Solve: a3/4 = 125 9)
10) Solve: 25
9
x+1
= 3
5
x-1
10)
11) Solve: e4x – 1 = (e3)-x 11)
12) Solve: 8x – 1 = 323x 12)
13) Solve: m-4 = 1
81
13)
14) Solve: 1
3
2x + 3
= 9x- 5 14)
1
15) Solve: ( 5 )x + 1 = 25x 15)
16) Solve: ex – 3 = 1
e6
x + 2
16)
17) The growth in the mouse population at a certain county dump can be
modeled by the exponential function A(t)= 906e0.012t, where t is the
number of months since the population was first recorded. Estimate the
population after 36 months.
17)
18) The decay of 938 mg of an isotope is given by A(t)= 938e-0.022t, where t
is time in years since the initial amount of 938 mg was present. Find the
amount (to the nearest milligram) left after 96 years.
18)
19) The sales of a mature product (one which has passed its peak) will
decline according to the function S(t) = S0e-at, where t is time in years
since the peak sales. Find the sales of a product 17 years after its peak
sales if a = 0.22 and S0 = 77,500.
19)
20) The number of reports of a certain virus has increased exponentially
since year 0. The number of cases can be approximated using the
function r(t) = 119 e0.008t, where t is the number of years since year 0.
Estimate the number of cases in year 40.
20)
21) An element decays at the rate of S(t) = se-0.048t, where s is the initial
amount in grams and t is the time in years since this initial amount was
present. If you have a 71-gram piece of this element, how many grams
will you have 5 years from now? Round your answer to the nearest
tenth of a gram.
21)
22) Solve: log5 125 = x 22)
23) Solve: log3 1
27
= x 23)
24) Solve: log7 712 = x 24)
25) Solve: logx 625 = 4 25)
2
26) Solve: x = 8log8 13 26)
27) Solve: x = log10 0.01 27)
28) Solve: x = log2
5
8 28)
29) Solve: logx 9 = – 2 29)
30) Solve: log4 x = 3 30)
31) Solve: log5 x = -3 31)
32) Solve: log(x – 5) 10 = 1 32)
33) Solve: log(x + 7) 11 = 1 33)
34) Solve: 8x – 32 = logx 1 34)
35) Suppose f(x) = logax and f(4) = 2. Find f(16). 35)
36) Suppose f(x) = logax and f(4) = 2. Find f 1
16
. 36)
37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 37)
38) Suppose f(x) = loga(x) and f(5) = 2. Find f 5
5
38)
39) Evaluate: 100log107 39)
40) Evaluate: log10(0.01)9 40)
41) Evaluate: 1000log1010 41)
42) Evaluate: log10(0.0001)10 42)
3
43) The growth in population of a city can be seen using the formula p(t) =
2148e0.008t, where t is the number of years. Use this formula to
calculate the population after 10 years.
43)
44) Suppose the government wants to impose a tax on fossil fuels to reduce
carbon emissions. The cost benefit is modeled by
ln(1 – P) = -0.0039 – 0.0051x, where x represents the dollars of tax per ton
of carbon emitted and P represents the percent reduction in emissions of
carbon. (P is in decimal form.) Determine P when x = 63. Round to three
decimal places.
44)
45) Suppose f(x) = 32.6 + 1.2log (x + 1) models salinity of ocean water to
depths of 1000 meters at a certain latitude. x is the depth in meters and
f(x) is in grams of salt per kilogram of seawater. Approximate the
salinity (to the nearest hundredth) when the depth is 771 meters.
45)
4
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
1) 1
4
2) {-3}
3) {-4}
4) {4}
5) {2}
6) {3}
7) {-3}
8) {-8, 8}
9) {625}
10) – 1
3
11) 1
7
12) – 1
4
13) {-3, 3}
14) 7
4
15) 1
3
16) – 9
7
17) 1396
18) 113
19) 1841 units
20) 164 cases
21) 55.9 g
22) {3}
23) {-3}
24) {6}
25) {5}
26) {13}
27) {-2}
28) 3
5
29) 1
3
30) {64}
5
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
31) 1
125
32) {15}
33) {4}
34) {4}
35) 4
36) -4
37) 6
38) -1
39) 49
40) -18
41) 1000
42) -40
43) 2327
44) 0.278
45) 36.07 g/kg
6
– Advanced Functions Questions
– Advanced Functions Answers
**## MATH110WK678DiscussionHelp.docx**
**WK6 Practice with advanced functions**
This discussion may require you to use exponents (superscripts) or log bases (subscripts). A short-cut that is handy for this is that both the superscript key (to make exponents) and the subscript key are in the drop-down menu next to the
U for underline.
For other mathematical symbols, follow the instructions for Using the Equation Editor.
Pick ONE of the problems from this collection "Advanced Functions Questions" that has not already been solved. Pretend that you are tutoring someone who has never seen these problems before and give a detailed demonstration of its solution.
**Note:** Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
Select Start a New Conversation and make the problem number the subject of your post. The answers are provided so don't just give an answer—we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order
to get credit. I will indicate in the grading comments if corrections need to be made. If you haven't received credit, first double-check for my grading comments. If everything looks OK, then email me asking me to check on it.
If I indicate that there is a problem, you must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses to other classmates are required** – your initial post is worth the full points.
**WK7 Conics are Everywhere!**
This week we will investigate conic shapes in the real world.
Begin by selecting Start a New Conversation. Research ONE example of a conic section in real life that has not already been used by a classmate.
Make your choice (Bouncing ball) the subject of your post, and then tell us in your own words about your find. Do not just make this up off the top of your head. The St Louis Arch, for example, is NOT a parabola—it is an inverted catenary.
To get credit for this Discussion, you
**must cite a source** confirming that your example is, indeed, a conic and not some other more exotic curve.
Using a personal example (My eyebrow) will not count unless you can cite a source verifying that eyebrows are parabolic.
You must also respond to 2 classmates' posts. You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another post or share an example from your own life related to the topic.
**WK8 Final Debriefing**
Now that it's the last week of the course, stop by this discussion and tell us what your take was on MATH110 and what your future educational plans are.
Select Start a New Conversation and start a new discussion thread using your name as the subject and then share your thoughts with us.
In terms of this class, you're the expert—what was hard, what was easy, what changes would improve things? Your comments can help us make this a better class for future generations!
In terms of the future – what's next? What classes are you taking in the upcoming semester? Have you decided on a major? How close are you to tossing that mortarboard skyward?
Please also respond to 2 classmates. This is a good time to chime in with advice if you have experience with a class that someone else is about to begin! Just remember to be constructive with comments on an open Discussion!
**## UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## AdvancedFunctionsQuestionsandAnswers1.pdf**
Advanced Functions
1) Solve: 4096x = 8 1)
2) Solve: 1
9
x
= 729 2)
3) Solve: 4
7
x
= 2401
256
3)
4) Solve: 4-x = 1
256
4)
5) Solve: 4(8 – 2x) = 256 5)
6) Solve: 3(6 – 3x) = 1
27
6)
7) Solve: 3(6 + 3x) = 1
27
7)
8) Solve: 4 = b2/3 8)
9) Solve: a3/4 = 125 9)
10) Solve: 25
9
x+1
= 3
5
x-1
10)
11) Solve: e4x – 1 = (e3)-x 11)
12) Solve: 8x – 1 = 323x 12)
13) Solve: m-4 = 1
81
13)
14) Solve: 1
3
2x + 3
= 9x- 5 14)
1
15) Solve: ( 5 )x + 1 = 25x 15)
16) Solve: ex – 3 = 1
e6
x + 2
16)
17) The growth in the mouse population at a certain county dump can be
modeled by the exponential function A(t)= 906e0.012t, where t is the
number of months since the population was first recorded. Estimate the
population after 36 months.
17)
18) The decay of 938 mg of an isotope is given by A(t)= 938e-0.022t, where t
is time in years since the initial amount of 938 mg was present. Find the
amount (to the nearest milligram) left after 96 years.
18)
19) The sales of a mature product (one which has passed its peak) will
decline according to the function S(t) = S0e-at, where t is time in years
since the peak sales. Find the sales of a product 17 years after its peak
sales if a = 0.22 and S0 = 77,500.
19)
20) The number of reports of a certain virus has increased exponentially
since year 0. The number of cases can be approximated using the
function r(t) = 119 e0.008t, where t is the number of years since year 0.
Estimate the number of cases in year 40.
20)
21) An element decays at the rate of S(t) = se-0.048t, where s is the initial
amount in grams and t is the time in years since this initial amount was
present. If you have a 71-gram piece of this element, how many grams
will you have 5 years from now? Round your answer to the nearest
tenth of a gram.
21)
22) Solve: log5 125 = x 22)
23) Solve: log3 1
27
= x 23)
24) Solve: log7 712 = x 24)
25) Solve: logx 625 = 4 25)
2
26) Solve: x = 8log8 13 26)
27) Solve: x = log10 0.01 27)
28) Solve: x = log2
5
8 28)
29) Solve: logx 9 = – 2 29)
30) Solve: log4 x = 3 30)
31) Solve: log5 x = -3 31)
32) Solve: log(x – 5) 10 = 1 32)
33) Solve: log(x + 7) 11 = 1 33)
34) Solve: 8x – 32 = logx 1 34)
35) Suppose f(x) = logax and f(4) = 2. Find f(16). 35)
36) Suppose f(x) = logax and f(4) = 2. Find f 1
16
. 36)
37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 37)
38) Suppose f(x) = loga(x) and f(5) = 2. Find f 5
5
38)
39) Evaluate: 100log107 39)
40) Evaluate: log10(0.01)9 40)
41) Evaluate: 1000log1010 41)
42) Evaluate: log10(0.0001)10 42)
3
43) The growth in population of a city can be seen using the formula p(t) =
2148e0.008t, where t is the number of years. Use this formula to
calculate the population after 10 years.
43)
44) Suppose the government wants to impose a tax on fossil fuels to reduce
carbon emissions. The cost benefit is modeled by
ln(1 – P) = -0.0039 – 0.0051x, where x represents the dollars of tax per ton
of carbon emitted and P represents the percent reduction in emissions of
carbon. (P is in decimal form.) Determine P when x = 63. Round to three
decimal places.
44)
45) Suppose f(x) = 32.6 + 1.2log (x + 1) models salinity of ocean water to
depths of 1000 meters at a certain latitude. x is the depth in meters and
f(x) is in grams of salt per kilogram of seawater. Approximate the
salinity (to the nearest hundredth) when the depth is 771 meters.
45)
4
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
1) 1
4
2) {-3}
3) {-4}
4) {4}
5) {2}
6) {3}
7) {-3}
8) {-8, 8}
9) {625}
10) – 1
3
11) 1
7
12) – 1
4
13) {-3, 3}
14) 7
4
15) 1
3
16) – 9
7
17) 1396
18) 113
19) 1841 units
20) 164 cases
21) 55.9 g
22) {3}
23) {-3}
24) {6}
25) {5}
26) {13}
27) {-2}
28) 3
5
29) 1
3
30) {64}
5
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
31) 1
125
32) {15}
33) {4}
34) {4}
35) 4
36) -4
37) 6
38) -1
39) 49
40) -18
41) 1000
42) -40
43) 2327
44) 0.278
45) 36.07 g/kg
6
– Advanced Functions Questions
– Advanced Functions Answers
**## MATH110WK678DiscussionHelp.docx**
**WK6 Practice with advanced functions**
This discussion may require you to use exponents (superscripts) or log bases (subscripts). A short-cut that is handy for this is that both the superscript key (to make exponents) and the subscript key are in the drop-down menu next to the
U for underline.
For other mathematical symbols, follow the instructions for Using the Equation Editor.
Pick ONE of the problems from this collection "Advanced Functions Questions" that has not already been solved. Pretend that you are tutoring someone who has never seen these problems before and give a detailed demonstration of its solution.
**Note:** Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
Select Start a New Conversation and make the problem number the subject of your post. The answers are provided so don't just give an answer—we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order
to get credit. I will indicate in the grading comments if corrections need to be made. If you haven't received credit, first double-check for my grading comments. If everything looks OK, then email me asking me to check on it.
If I indicate that there is a problem, you must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses to other classmates are required** – your initial post is worth the full points.
**WK7 Conics are Everywhere!**
This week we will investigate conic shapes in the real world.
Begin by selecting Start a New Conversation. Research ONE example of a conic section in real life that has not already been used by a classmate.
Make your choice (Bouncing ball) the subject of your post, and then tell us in your own words about your find. Do not just make this up off the top of your head. The St Louis Arch, for example, is NOT a parabola—it is an inverted catenary.
To get credit for this Discussion, you
**must cite a source** confirming that your example is, indeed, a conic and not some other more exotic curve.
Using a personal example (My eyebrow) will not count unless you can cite a source verifying that eyebrows are parabolic.
You must also respond to 2 classmates' posts. You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another post or share an example from your own life related to the topic.
**WK8 Final Debriefing**
Now that it's the last week of the course, stop by this discussion and tell us what your take was on MATH110 and what your future educational plans are.
Select Start a New Conversation and start a new discussion thread using your name as the subject and then share your thoughts with us.
In terms of this class, you're the expert—what was hard, what was easy, what changes would improve things? Your comments can help us make this a better class for future generations!
In terms of the future – what's next? What classes are you taking in the upcoming semester? Have you decided on a major? How close are you to tossing that mortarboard skyward?
Please also respond to 2 classmates. This is a good time to chime in with advice if you have experience with a class that someone else is about to begin! Just remember to be constructive with comments on an open Discussion!
**## UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## AdvancedFunctionsQuestionsandAnswers1.pdf**
Advanced Functions
1) Solve: 4096x = 8 1)
2) Solve: 1
9
x
= 729 2)
3) Solve: 4
7
x
= 2401
256
3)
4) Solve: 4-x = 1
256
4)
5) Solve: 4(8 – 2x) = 256 5)
6) Solve: 3(6 – 3x) = 1
27
6)
7) Solve: 3(6 + 3x) = 1
27
7)
8) Solve: 4 = b2/3 8)
9) Solve: a3/4 = 125 9)
10) Solve: 25
9
x+1
= 3
5
x-1
10)
11) Solve: e4x – 1 = (e3)-x 11)
12) Solve: 8x – 1 = 323x 12)
13) Solve: m-4 = 1
81
13)
14) Solve: 1
3
2x + 3
= 9x- 5 14)
1
15) Solve: ( 5 )x + 1 = 25x 15)
16) Solve: ex – 3 = 1
e6
x + 2
16)
17) The growth in the mouse population at a certain county dump can be
modeled by the exponential function A(t)= 906e0.012t, where t is the
number of months since the population was first recorded. Estimate the
population after 36 months.
17)
18) The decay of 938 mg of an isotope is given by A(t)= 938e-0.022t, where t
is time in years since the initial amount of 938 mg was present. Find the
amount (to the nearest milligram) left after 96 years.
18)
19) The sales of a mature product (one which has passed its peak) will
decline according to the function S(t) = S0e-at, where t is time in years
since the peak sales. Find the sales of a product 17 years after its peak
sales if a = 0.22 and S0 = 77,500.
19)
20) The number of reports of a certain virus has increased exponentially
since year 0. The number of cases can be approximated using the
function r(t) = 119 e0.008t, where t is the number of years since year 0.
Estimate the number of cases in year 40.
20)
21) An element decays at the rate of S(t) = se-0.048t, where s is the initial
amount in grams and t is the time in years since this initial amount was
present. If you have a 71-gram piece of this element, how many grams
will you have 5 years from now? Round your answer to the nearest
tenth of a gram.
21)
22) Solve: log5 125 = x 22)
23) Solve: log3 1
27
= x 23)
24) Solve: log7 712 = x 24)
25) Solve: logx 625 = 4 25)
2
26) Solve: x = 8log8 13 26)
27) Solve: x = log10 0.01 27)
28) Solve: x = log2
5
8 28)
29) Solve: logx 9 = – 2 29)
30) Solve: log4 x = 3 30)
31) Solve: log5 x = -3 31)
32) Solve: log(x – 5) 10 = 1 32)
33) Solve: log(x + 7) 11 = 1 33)
34) Solve: 8x – 32 = logx 1 34)
35) Suppose f(x) = logax and f(4) = 2. Find f(16). 35)
36) Suppose f(x) = logax and f(4) = 2. Find f 1
16
. 36)
37) Suppose f(x) = loga(x) and f(7) = 2. Find f(343). 37)
38) Suppose f(x) = loga(x) and f(5) = 2. Find f 5
5
38)
39) Evaluate: 100log107 39)
40) Evaluate: log10(0.01)9 40)
41) Evaluate: 1000log1010 41)
42) Evaluate: log10(0.0001)10 42)
3
43) The growth in population of a city can be seen using the formula p(t) =
2148e0.008t, where t is the number of years. Use this formula to
calculate the population after 10 years.
43)
44) Suppose the government wants to impose a tax on fossil fuels to reduce
carbon emissions. The cost benefit is modeled by
ln(1 – P) = -0.0039 – 0.0051x, where x represents the dollars of tax per ton
of carbon emitted and P represents the percent reduction in emissions of
carbon. (P is in decimal form.) Determine P when x = 63. Round to three
decimal places.
44)
45) Suppose f(x) = 32.6 + 1.2log (x + 1) models salinity of ocean water to
depths of 1000 meters at a certain latitude. x is the depth in meters and
f(x) is in grams of salt per kilogram of seawater. Approximate the
salinity (to the nearest hundredth) when the depth is 771 meters.
45)
4
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
1) 1
4
2) {-3}
3) {-4}
4) {4}
5) {2}
6) {3}
7) {-3}
8) {-8, 8}
9) {625}
10) – 1
3
11) 1
7
12) – 1
4
13) {-3, 3}
14) 7
4
15) 1
3
16) – 9
7
17) 1396
18) 113
19) 1841 units
20) 164 cases
21) 55.9 g
22) {3}
23) {-3}
24) {6}
25) {5}
26) {13}
27) {-2}
28) 3
5
29) 1
3
30) {64}
5
Answer Key
Testname: FORUM ADVANCED FUNCTIONS
31) 1
125
32) {15}
33) {4}
34) {4}
35) 4
36) -4
37) 6
38) -1
39) 49
40) -18
41) 1000
42) -40
43) 2327
44) 0.278
45) 36.07 g/kg
6
– Advanced Functions Questions
– Advanced Functions Answers