Question 1

Which of the following is an exponential function?

Accepted Answer

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

Question 2

Given the function $$f(x) = 3(1.5)^x$$, what is the value of $$f(4)$$?

Accepted Answer

$$f(4) = 15.1875$$

Question 3

Which statement correctly describes the difference between a polynomial and an exponential function?

Accepted Answer

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

Question 4

Evaluate $$f(x) = 2^x$$ for $$x = 3.14. $$Round your answer to three decimal places.

Accepted Answer

$$8.815$$

Question 5

Which of the following functions is NOT an exponential function?

Accepted Answer

$$f(x) = x$$^{10+1}$$

Question 6

A scientist models the growth of bacteria with the function $$N(t) = 500 \cdot 2^t$$, where $$t is $$time in hours. How many bacteria will there be after 5 hours?

Accepted Answer

$$16,000$$

Question 7

Which of the following is the correct base and exponent for the exponential function $$f(x) = (-2)^x$$?

Accepted Answer

Base: $$-2$$, Exponent: $$x$$

Question 8

If $$f(x) = 2^x$$ and $$g(x) = x^2$, which function grows faster as x$ increases?

Accepted Answer

$$f(x)$$ grows faster for large $$x$$

Question 9

A medication's concentration in the bloodstream decreases according to $$C(t) = 100 \cdot (0.8)^t$$, where $$t is in $$hours. What is the concentration after 3 hours?

Accepted Answer

$$51.2$$

Question 10

Which of the following is the correct way to evaluate $$f(x) = 2^x$$ for $$x = -3$$?

Accepted Answer

$$2^{-3} = 0.125$

Question 11

Which function represents exponential decay?

Accepted Answer

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

Question 12

A population doubles every year. If the initial population is 1,000, which function models the population after $$t$$ years?

Accepted Answer

$$P(t) = 1,000 \cdot 2^t$$

Question 13

Which of the following is the correct evaluation of $$f(x) = (\frac{1}{4})^x$$ for $$x = 2$$?

Accepted Answer

$$0.0625$$

Question 14

Which function is a polynomial?

Accepted Answer

$$f(x) = x^2$

Question 15

If $$f(x) = 2^x$$, what is $$f(0)$$?

Accepted Answer

$$1$$

Question 16

Which of the following functions has a constant base and a variable exponent?

Accepted Answer

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

Question 17

A radioactive substance decays according to $$A(t) = 200 \cdot (0.9)^t. $$What is the amount left after 2 hours?

Accepted Answer

$$162$$

Question 18

Which of the following is the correct evaluation of $$f(x) = 10$$^{x+1}$$ for x = 2$?

Accepted Answer

$$1,000$$

Question 19

Which function best models the depreciation of a car's value, losing 20% of its value each year?

Accepted Answer

$$V(t) = V_0$ \cdot (0.8)^t$$

Question 20

Which of the following is NOT a property of exponential functions?

Accepted Answer

The exponent is always a constant.

Polynomial and Exponential Functions: Definitions, Properties, and Examples

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