Question 1

Which of the following best describes the horizontal asymptote of any exponential function of the form $$f(x) = b^x$$ where $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

$$y = 0$$

Question 2

Evaluate the exponential function $$f(x) = 2^x at$$ $$x = -3.$$

Accepted Answer

$$f(-3) = \frac{1}{8}$$

Question 3

Which of the following graphs represents an exponential decay function?

Accepted Answer

$$f(x) = 0.5^x$$

Question 4

If the population of gray wolves in a region is modeled by $$P(t) = 150e$$^{0.04t}$$, where t$ is in years, what is the population after 10 years? (Round to the nearest whole number)

Accepted Answer

$$P(10) = 150e$$^{0.4}$$ \approx 224$$

Question 5

Which of the following is the correct formula for compound interest compounded $$n$$ times per year?

Accepted Answer

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

Question 6

A $$\1000$ investment earns 5$$\%$$ annual interest compounded quarterly. What is the value after 3 years? (Use A = P$$\left(1 + \frac{r}{n}\$$right)^{nt}$ and round to the nearest cent)

Accepted Answer

$$A \approx \1157.63$

Question 7

Which transformation will shift the graph of $$f(x) = 3^x$$ one unit to the right?

Accepted Answer

$$f(x) = 3$$^{x-1}$$

Question 8

Which of the following statements is true about the function $$f(x) = b^x$$ for $$0 \u003c b \u003c 1$$?

Accepted Answer

The function is decreasing for all $$x.$$

Question 9

Evaluate $$f(x) = e^x at$$ $$x = 2. ($$Use $$e \approx 2.718$$ and round to two decimal places)

Accepted Answer

$$e^2$$ \approx 7.39$$

Question 10

A scientist models bacteria growth with $$N(t) = 500e$$^{0.3t}$$. How many bacteria are present after 5 hours? (Round to the nearest whole number)

Accepted Answer

$$N(5) \approx 500e$$^{1.5}$$ \approx 2241$$

Question 11

Which of the following best describes the effect of multiplying an exponential function $$f(x) = b^x by a $$constant $$a \u003e 1$$?

Accepted Answer

The graph is stretched vertically by a factor of $$a.$$

Question 12

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

Accepted Answer

$$f(-2) = \frac{1}{16}$$

Question 13

A savings account offers continuous compounding at an annual rate of $$6\%. If $$you deposit $$\2000$, how much will you have after 4 years? (Use A$$ = $$Pe^{rt}$ and round to the nearest cent)

Accepted Answer

$$A \approx \2546.50$

Question 14

Which of the following is NOT a property of all exponential functions $$f(x) = b^x$$ with $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

The range is all real numbers.

Question 15

Suppose $$f(x) = 2^x$$ and $$g(x) = 2$$^{x-3}$$. How is the graph of g(x$$)$$ related to f(x$$)$$?

Accepted Answer

It is shifted 3 units to the right.

Exponential and Logarithmic Functions: Exponential Functions

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