Question 1

Which of the following is the correct equation for the exponential function whose graph passes through the points (0, 1), (1, 2), (2, 4), and (3, 8)?

Accepted Answer

$$y = 2^x$$

Question 2

Given the exponential function $$f(x) = b^x$$, which of the following statements is TRUE if $$0 \u003c b \u003c 1$$?

Accepted Answer

The function is decreasing for all $$x$$

Question 3

Which of the following is NOT an exponential function?

Accepted Answer

$$g(x) = x^2$

Question 4

What is the horizontal asymptote of the function $$f(x) = 5^x$$?

Accepted Answer

$$y = 0$$

Question 5

If $$A = P(1 + \frac{r}{n}$$)^{nt}$$, what is the value of A$ after 5 years for a $10,000 deposit at 9% annual interest compounded monthly?

Accepted Answer

$$A = 10,000(1 + 0.0075$$)^{60}$$

Question 6

Which of the following points is NOT on the graph of $$y = 4^x$$?

Accepted Answer

$$(2, 8)$$

Question 7

The number $$e is $$defined as the value that $$1 + \frac{1}{n}$$ raised to the $$nth $$power approaches as $$n$$ becomes large. What is the approximate value of $$e to $$five decimal places?

Accepted Answer

$$e \approx 2.71828$$

Question 8

Which of the following best describes the domain and range of $$f(x) = e^x$$?

Accepted Answer

Domain: $$x \in (-\infty, \infty)$$; Range: $$y \in (0, \infty)$$

Question 9

If $$A = Pe$$^{rt}$$, what is the balance after 3 years for a 2340$ deposit at 3.1% annual interest compounded continuously?

Accepted Answer

$$A = 2340 \cdot e$$^{0.093}$$

Question 10

Which of the following graphs represents a decreasing exponential function?

Accepted Answer

$$y = \frac{1}{2}^x$$

Question 11

If $$f(x) = b^x$$ and $$f(-1) = \frac{1}{b}$$, what is $$f(-2)$$?

Accepted Answer

$$b^{-2}$$ = \frac{1}{$$b^2$$}$$

Question 12

Which of the following is the correct formula for the future value of $$9000 at$$ $$6\%$$ interest compounded quarterly for $$10$$ years?

Accepted Answer

$$A = 9000(1 + \frac{0.06}{4}$$)^{40}$$

Question 13

If $$f(x) = 6^x$$, what is the value of $$f(-1)$$?

Accepted Answer

$$\frac{1}{6}$$

Question 14

Which of the following is a real-life situation that can be modeled by an exponential function?

Accepted Answer

Population growth

Question 15

If $$f(x) = 3^x$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, 1)$$

Question 16

Which of the following is the correct formula for continuous compounding?

Accepted Answer

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

Question 17

If $$f(x) = b^x$$ and $$b \u003e 1$$, which of the following best describes the graph?

Accepted Answer

The graph increases as $$x$$ increases

Question 18

Tony and Matt both invest $$4,500 at$$ $$6\%$$ annual interest for $$10$$ years. Tony's account is compounded quarterly, Matt's is compounded continuously. Who made the better investment?

Accepted Answer

Matt, because continuous compounding yields more than quarterly compounding

Exponential and Logarithmic Functions: Core Concepts and Applications

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