Name: ________________________ Class: ___________________ Date: __________
ID: A
Exponential Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Graph the exponential function.
____
1. y = 3 (1.9)
a.
x
b.
____
d.
2. An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model
the quail population.
a. f(x) = 895(1.07) x
c. f(x) = 895(0.07) x
b.
____
c.
f(x) = 895(7) x
d.
f(x) = (895 ⋅ 0.07)
x
3. Find the annual percent increase or decrease that y = 0.35(2.3) x models.
a. 230% increase
c. 30% decrease
b. 130% increase
d. 65% decrease
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Name: ________________________
____
____
____
____
ID: A
4. Solve 15 2x = 36. Round to the nearest ten-thousandth.
a. 0.6616
b. 2.6466
c. 1.7509
d.
1.9091
5. Solve ln(2x − 1) = 8. Round to the nearest thousandth.
a. 1,489.979
b. 2,979.958
c. 2,981.458
d.
1,490.979
6. Solve ln 2 + ln x = 5.
a. 50,000
b.
74.2
c.
10
d.
3
7. Solve ln x − ln 6 = 0.
a. 6
b.
6e
c.
e6
d.
ln 6
Use natural logarithms to solve the equation. Round to the nearest thousandth.
____
8. 6e 4x − 2 = 3
a. –0.448
b.
0.327
c.
0.067
d.
–0.046
3
4
–0.288
b.
–0.275
c.
0.275
d.
0.288
____ 10. e 2x = 1.4
a. –1.664
b.
0.073
c.
0.168
d.
0.190
____
9. e x =
a.
____ 11. The amount of money in an account with continuously compounded interest is given by the formula
A = Pe rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the
nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded
continuously at 6.2%. Round to the nearest tenth.
a. 1.1 yr
b. 6.9 yr
c. 11.2 yr
d. 0.6 yr
Essay
12. Suppose you invest $580 at 10% 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 reach $3600? Show your work.
13. The function y = 120(1.02) x models the kindergarten population y of a certain elementary school x years
after the year 2000. Graph the function on your graphing calculator. Explain how to use the calculator to
estimate when the kindergarten population will reach 142 and state the year that you estimate.
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