Question 1

Which of the following best describes an exponential function?

Accepted Answer

A function where the variable is in the exponent, such as $$f(x) = a \cdot b^x$$

Question 2

Suppose a population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 2$$^{t/3}$$

Question 3

Which of the following is the inverse of the exponential function $$f(x) = 3^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_3$${x}$$

Question 4

A medication is administered to a patient and the amount in the bloodstream decreases by 20% each hour. If the initial dose is 500 mg, how much remains after 5 hours?

Accepted Answer

$$500 \cdot (0.8)^5$

Question 5

Which of the following graphs represents exponential decay?

Accepted Answer

A curve that decreases rapidly at first and then levels off as $$x$$ increases

Question 6

Given the function $$f(x) = 2^x$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 7

If $$f(x) = 3^x$$, which transformation results in $$g(x) = 3$$^{x-2}$$ + 4$$?

Accepted Answer

Shift right 2 units and up 4 units

Question 8

The value of the mathematical constant $$e is $$approximately:

Accepted Answer

$$2.718$$

Question 9

A car depreciates in value by 15% each year. If the car was purchased for $20,000, what is its value after 3 years?

Accepted Answer

$$20,000 \cdot (0.85)^3$

Question 10

Which of the following data sets is best modeled by an exponential function?

Accepted Answer

A population that triples every decade

Question 11

Given the exponential function $$f(x) = a \cdot b^x$$, which value of $$b$$ indicates exponential growth?

Accepted Answer

$$b \u003e 1$$

Question 12

Which of the following is the correct formula for continuously compounded interest?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 13

A scientist is studying the decay of a radioactive substance. The amount remaining after $$t$$ years is modeled by $$A(t) = 100 \cdot (0.92)^t. $$What is the percent decrease per year?

Accepted Answer

8%

Question 14

Which of the following statements is true about the domain and range of an exponential function $$f(x) = a \cdot b^x$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 15

If $$f(x) = 4^x$$, what is $$f(-2)$$?

Accepted Answer

$$\frac{1}{16}$$

Question 16

Which of the following best describes the transformation from $$f(x) = 2^x to$$ $$g(x) = -2^x + 3$$?

Accepted Answer

Reflect over the $$x-$$axis and shift up 3 units

Question 17

A movie's box office revenue decreases by 40% each week after release. If the opening weekend revenue is $$10$$ million, what is the revenue after 3 weeks?

Accepted Answer

$$10 \cdot (0.6)^3$

Question 18

Which of the following is NOT a characteristic of exponential growth?

Accepted Answer

The rate of increase is constant

Question 19

Given the data set: $$x = 0, 1, 2, 3$$ and $$y = 5, 10, 20, 40$$, which type of function best models the data?

Accepted Answer

Exponential

Exponential and Logarithmic Functions: Study Guide

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