Math 176 calculus multi-part question

Math 176 calculus multi-part questionMath 176 – Exam 3 (Chapters 6) Page 1 of 4 Name: ________________________
Directions: Be sure to label your work with the number and/or letter it corresponds to, and circle final answers
when possible. Answers without enough supporting work may not receive full credit! This is a Take Home Test
and as such I expect you to use all the notes, google searches, etc that you need to answer the questions to the
best of YOUR ability. I do say YOUR ability because I want to know what you can comfortably do, and what you
may not be able to do yet so I can better help you prepare for the cumulative final. Please, do not share your
answers with anyone, and be kind to yourself by giving yourself enough time to submit the test on time. Enjoy!
1. Write the equation of an exponential function that passes through the points (2, −12) and (3, −24).
Be sure to show your work, and feel free to check your answer using your calculator.
2. If you invest $1000 at an annual interest rate of 5%.
a. How much will you have in the account 15 years later if interest is compounded quarterly (4 times per
year). Round to the nearest cent.
b. Suppose that the interest is compounded continuously, how much more would you have in the account
after 15 years?
3. Write a basic exponential function for a car that sells for $16000, and each year loses 17.6% of its value.
4. A freezer has a temperature of 14 degrees Fahrenheit. An ice-cube tray full of water is placed in the freezer.
The temperature of the water can be found using the function ?(?) = ??
−?? + 14, where ? is time in
minutes, ? is a constant, and ? = 0.045. After 15 minutes the water has a temperature of 40 degrees.
a. Find the value of constant ? rounded to the nearest degree and write the complete function.
b. What was the initial temperature of the water? Round your answer to the nearest degree.
Math 176 – Exam 3 (Chapters 6) Page 2 of 4 Name: ________________________
5. Radioiodine therapy is a nuclear medicine treatment that can be used to treat thyroid cancer.
The therapy involves the use of Iodine-131 which has a half-life of 8.10 days.
a. Find the rate of decay for Iodine-131. Round to four decimal places.
b. How long will it take a 50.00g to decay to 6.25 g? Round to one decimal place.
6. Graph the original function and its transform. Include all asymptotes and intercepts (if possible).
Get as many clear points on the graph as you can (make a table of ?- and ?-values if needed), and describe in
words the transformation of ?(?) represented by ?(?) (shift, stretch/compression, reflection, etc. in what
direct and by how much).
a. ?(?) = 4
?
and ?(?) = 4
?+2 − 3 b. ?(?) = (
1
2
)
?
and ?(?) = (
1
2
)
?−3
+ 2
7. Find the value of each expression without using a calculator.
a. ???4
(1) = b. ???2
(64) =
c. ???5 (
1
125) = d. ???7
(7) =
Math 176 – Exam 3 (Chapters 6) Page 3 of 4 Name: ________________________
e. ????(?
−4
) = f. 6
???6
(9) =
8. Find the domain of each function by hand
a. ? = ln(? + 31) − 17 b. ? = ln(−2? + 24) + 8
9. Let ?(?) = ???5(?). Write the equation of the function if it is shifted down 7 units, shifted 4 units to the left,
and vertically reflected over the x-axis.
10. Rewrite each of the following as an exponential equation. DO NOT SOLVE!
a. log(7) = 0.845 b. ???3
(?) = −2
11. Rewrite each of the following as a logarithmic equation. DO NOT SOLVE!
a. 2
−5 =
1
32
b. ?
? = 6
12. Rewrite as a single logarithm: 2???7
(?) + 6???7(?)
13. Rewrite as a sum/difference of logarithms: ?? (
7
8?
4
)
Math 176 – Exam 3 (Chapters 6) Page 4 of 4 Name: ________________________
14. Solve each equation and find exact solutions only.
a. ????
(1296) = 4 b. ln(2? + 5) = 3.4
c. ???8
(?
2 − 2?) = 1 d. ???2
(?) − ???2
(3? + 5) = 4
e. 4
?+7 = 3 f. 5?
3? = 22