Question 1

Which of the following is the correct general form of an exponential function?

Accepted Answer

$$f(x) = a^x$$

Question 2

Given the function $$f(x) = 2^x$$, what is the base and what is the power?

Accepted Answer

Base: $$2$$, Power: $$x$$

Question 3

Which of the following functions is NOT an exponential function?

Accepted Answer

$$f(x) = x^3$

Question 4

Evaluate the exponential function $$f(x) = 4^x at$$ $$x = 2.$$

Accepted Answer

$$16$$

Question 5

Which of the following best describes the difference between a polynomial and an exponential function?

Accepted Answer

A polynomial has a variable as the base and a constant as the exponent, while an exponential function has a constant as the base and a variable as the exponent.

Question 6

If $$f(x) = 3$$^{2x}$$, what is f(1$$)$$?

Accepted Answer

$$9$$

Question 7

Which of the following real-life scenarios can be modeled by an exponential function?

Accepted Answer

The growth of a bacteria population that doubles every hour.

Question 8

Given $$f(x) = 5^x$$, what is $$f(-2)$$?

Accepted Answer

$$\frac{1}{25}$$

Question 9

Which of the following is the correct evaluation of $$f(x) = 2$$^{x+1}$$ at x = 3$?

Accepted Answer

$$16$$

Question 10

Suppose a radioactive substance decays according to the function $$N(t) = N_0$ \cdot (0.5)^t$$, where $$N_0 is $$the initial amount and $$t is $$time in hours. If $$N_0 = 100$ grams, how much remains after 3 hours?

Accepted Answer

$$12.5$$ grams

Question 11

Which of the following is an exponential function with base $$e$$?

Accepted Answer

$$f(x) = e^x$$

Question 12

If $$f(x) = 10^x$$, what is $$f(0)$$?

Accepted Answer

$$1$$

Question 13

Which of the following is the correct evaluation of $$f(x) = 3$$^{x-1}$$ at x = 4$?

Accepted Answer

$$27$$

Question 14

A scientist models the spread of a virus with $$V(t) = 100 \cdot 2^t$$, where $$t is in $$days. How many cases will there be after 5 days?

Accepted Answer

$$3200$$

Question 15

Which of the following is the correct base and power for the function $$f(x) = (\frac{1}{2})^x$$?

Accepted Answer

Base: $$\frac{1}{2}$$, Power: $$x$$

Introduction to Exponential Functions

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