chapter 7 review

1. Graph the following exponential functions:
a. y = 2(4.1)x
c. y = -3(5)x - 1 + 2
b. y = 3(4)x
d. y = 4(3)x + 4 – 1
2. Which exponential function matches the graph below?
3. For an annual rate of change of -54%, what is the corresponding growth or decay factor?
4. Evaluate: e2.45
5. If you invest $1250 at an annual interest rate of 2.6% compounded continuously, how much will you
have in the account after 6 years?
6. How much money invested at 7% compounded continuously for 3 years will yield $600?
7. Write the equation in logarithm form:
a. 65/6 = 27
b. 2x = 81
8. Evaluate the logarithm:
a. log749
b. log16 4
c. log8512
9. Write in exponential form: log48 = x
10. Graph the following logarithm functions:
a. y = log3x
11. Write the expression as a single logarithm:
12. Expand the logarithmic expression:
b. y = log(x + 2) – 4
13. Use the properties of logarithms to evaluate: log24 + log216 – log28
14. Use change of base formula to solve: 115x = 33
15. Solve:
16. Simplify: ln e7
17. Solve:
2e3x + 4 = 8
b. ex = 9
18. The table shows the number of squirrels in a particular forest t years after a forest fire.
a. Explain how the population of squirrels is changing each year.
b. Write a function to model the situation. Explain what each number represents.
19. Suppose you invest $380 at 5% compounded continuously.
a. Write an exponential function to model the amount in your investment account.
b. Explain what each value in the function model represents.
c. In how many years will the total each $1600? Show your work.
20. The exponential decay graph shows the expected depreciation for a new 4-wheeler, selling for $7000,
over 10 years.
a. Write an exponential function for the graph.
b. Use the function in part a to find the value of the 4-wheeler after 7.5 years.
21. In a particular region of a national park, there are currently 500 bear, and the population is increasing at
an annual rate of 14%.
a. Write an exponential function to model the deer population.
b. Explain what each value in the model represents.
c. Predict the number of bear that will be in the region after 5 years. Show your work.