Q: A population of bacteria triples every 2 hours. If the initial population is 500, what is the population after 6 hours?

$$500 \times 3$$^{3}$$ = 13,500$$

Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = 2^x$$?

Accepted Answer

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

Question 2

Suppose a $$1000 investment earns 1.5\%$$ annual interest, compounded quarterly, for 10 years. What is the final amount in the account? (Use $$A = P(1 + \frac{r}{n}$$)^{nt}$$)

Accepted Answer

$$A = 1000(1.00375$$)^{40}$$ \approx 1161.51$$

Question 3

Which of the following statements about the exponential function $$f(x) = a^x$$ with $$a \u003e 1 is $$TRUE?

Accepted Answer

The function is increasing and continuous on $$(-\infty, \infty).$$

Question 4

If $$f(x) = (\frac{1}{2})^x$$, which of the following describes its graph?

Accepted Answer

It is decreasing and continuous on $$(-\infty, \infty)$$, with a horizontal asymptote at $$y = 0.$$

Question 5

Solve the exponential equation: $$5^{2x} = 125$. What is the value of x$?

Accepted Answer

$$x = 1.5$$

Question 6

A medication decays in the bloodstream according to $$C(t) = 100e$$^{-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

$$C(5) = 100e$$^{-1}$$ \approx 36.79 mg/L$$

Question 7

Which of the following is the correct formula for the amount $$A$$ after $$t$$ years with continuous compounding at rate $$r$$?

Accepted Answer

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

Question 8

If $$f(x) = 2^x$$ and $$g(x) = -2^x$$, how does the graph of $$g(x)$$ relate to $$f(x)$$?

Accepted Answer

It is a reflection of $$f(x)$$ across the $$x-$$axis.

Question 9

Solve the inequality $$3^x \u003c 81.$$

Accepted Answer

$$x \u003c 4$$

Question 10

A population of bacteria triples every 2 hours. If the initial population is 500, what is the population after 6 hours?

Accepted Answer

$$500 	imes 3$$^{3}$$ = 13,500$$

Question 11

Which of the following is NOT a property of exponents for $$a \u003e 0$$, $$a 
eq 1$$?

Accepted Answer

$$a^x is $$always negative for $$x \u003c 0$$

Question 12

If $$f(x) = 2$$^{x+3}$$, how is its graph related to f(x) = 2^x$?

Accepted Answer

It is translated 3 units to the left.

Question 13

Suppose the risk of a disease increases exponentially after age 40 as $$r(x) = r_0$(1.11)^x$$, where $$x is $$years after 40. If $$r_0 is $$the risk at age 40, what is the risk at age 75 compared to age 40?

Accepted Answer

About 39 times greater

Question 14

Which of the following best describes the range of $$f(x) = -2^x$$?

Accepted Answer

$$(-\infty, 0)$$

Question 15

If $$A = Pe$$^{rt}$$, what is the value of A$ after 10 years for P = 1000$, r = 0.015$, and t = 10$?

Accepted Answer

$$A = 1000e$$^{0.15}$$ \approx 1161.83$$

Question 16

Which of the following is the horizontal asymptote of $$f(x) = 2^x$$?

Accepted Answer

$$y = 0$$

Question 17

Solve the exponential equation: $$3^{-x} = 81$.

Accepted Answer

$$x = -4$$

Question 18

A $$1000$$ investment earns $$1.5\%$$ annual interest, compounded continuously, for $$10$$ years. How much more interest is earned compared to quarterly compounding?

Accepted Answer

$$0.32$$

Question 19

Which of the following transformations results in the graph of $$f(x) = 2^x$$ being shifted up by 3 units?

Accepted Answer

$$f(x) = 2^x + 3$$

Exponential Functions: Properties, Graphs, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards