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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