Question 1

Which of the following is the correct definition of an exponential function?

Accepted Answer

$$f(x) = a^x$$, where $$x is a $$real number, $$a \u003e 0$$ and $$a 
eq 1$$

Question 2

What is the horizontal asymptote of the exponential function $$f(x) = 2^x$$?

Accepted Answer

$$y = 0$$

Question 3

Suppose you invest $$P = 50,000 at an $$annual interest rate of $$r = 4\%$$ compounded quarterly. Which formula gives the amount $$A$$ after $$t$$ years?

Accepted Answer

$$A = 50,000 \left(1 + \dfrac{0.04}{4}\$$right)^{4t}$$

Question 4

Which transformation occurs to the graph of $$y = e^x to $$obtain $$y = e$$^{x+3}$$?

Accepted Answer

Shift left 3 units

Question 5

If $$f(x) = \left(\dfrac{1}{2}\right)^x$$, which statement best describes its graph compared to $$f(x) = 2^x$$?

Accepted Answer

It is a reflection of $$f(x) = 2^x$$ across the $$y-$$axis

Question 6

Given $$f(x) = 5 - 0.5^x$$, which of the following describes the sequence of transformations applied to $$y = 2^x$$?

Accepted Answer

Reflection across the $$y-$$axis, reflection across the $$x-$$axis, then shift up 5 units

Question 7

Which of the following statements about the number $$e is $$TRUE?

Accepted Answer

$$e is $$approximately $$2.71828$$ and is an irrational constant

Question 8

A population of bacteria doubles every 3 hours. If the initial population is $$P_0$$, which exponential function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2$$^{t/3}$$

Question 9

Which of the following is the value of $$e^3$$ rounded to four decimal places?

Accepted Answer

$$e^3$$ \approx 20.0855$$

Question 10

For the function $$f(x) = 2$$^{x-2}$$, what transformation has been applied to f(x) = 2^x$?

Accepted Answer

Shift right 2 units

Question 11

If $$A(t) = 100,000(1.0325$$)^{2t}$$, what is the value of A(8$$)$$?

Accepted Answer

$$A(8) \approx 166,817.25$$

Question 12

Which of the following best describes the end behavior of $$f(x) = 0.4^x as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x)$$ approaches 0

Question 13

Which of the following is the correct formula for the amount $$A$$ after $$t$$ years if $$P is $$invested at rate $$r$$ compounded $$n$$ times per year?

Accepted Answer

$$A = P \left(1 + \dfrac{r}{n}\$$right)^{nt}$$

Question 14

Which of the following describes the graph of $$f(x) = e$$^{-x}$$ compared to f(x) = e^x$?

Accepted Answer

It is a reflection across the $$y-$$axis

Question 15

A medication decays exponentially in the bloodstream according to $$C(t) = 50e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) \approx 18.39 mg/L$$

Question 16

Which of the following is NOT a property of exponential functions $$f(x) = a^x$$ with $$a \u003e 1$$?

Accepted Answer

The function has a maximum value at $$x = 0$$

Question 17

If $$f(x) = 1 - e$$^{-2x}$$, which of the following describes the transformations applied to y = e^x$?

Accepted Answer

Horizontal shrinking, reflection across $$y-$$axis, reflection across $$x-$$axis, and shift up 1 unit

Question 18

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$, where N_0$ is the initial amount and k$ is a positive constant. If N_0$ = 100$$ grams and $$k = 0.1$$, how much remains after 10 years?

Accepted Answer

$$N(10) \approx 36.79$$ grams

Question 19

If $$f(x) = 3.57^x$$, what is the value of $$f(2)$$ rounded to two decimal places?

Accepted Answer

$$f(2) \approx 12.75$$

Exponential Functions and Their Graphs

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