Practice Exponential Function in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An exponential function has the form f(x)=a⋅bx where b>0, b≠1. The variable is in the exponent, not the base.

Growth (or decay) that multiplies by a constant factor repeatedly.

Showing a random 20 of 50 problems.

Example 1

challenge
Two species of bacteria start with the same population. Species A doubles every 4 hours, Species B triples every 9 hours. After how many hours do their populations match again, other than at t=0? Express the smallest positive answer.

Example 2

hard
A bacterial culture grows from 500 to 32,000 in 5 hours. Assuming exponential growth, find the doubling time.

Example 3

easy
What is the initial value a in f(x)=7⋅2x?

Example 4

medium
What is the range of f(x)=2x?

Example 5

easy
Is f(x)=2x or g(x)=x2 the exponential function?

Example 6

medium
The population of a town grows from 5000 to 6655 in 3 years exponentially. Find the annual growth rate.

Example 7

easy
Evaluate 25.

Example 8

hard
For what value of b does f(x)=bx pass through (3,64)?

Example 9

easy
A bacteria population starts at 500 and doubles every 3 hours. Write an exponential model and find the population after 9 hours.

Example 10

medium
Solve 32x−1=81.

Example 11

challenge
If ax=3 and ay=5, find a2x+y.

Example 12

medium
A quantity halves every 5 years from 80 grams. How much remains after 15 years?

Example 13

easy
What is the domain of f(x)=2x?

Example 14

medium
Solve 5x+1=125.

Example 15

medium
Simplify (23)2.

Example 16

challenge
Solve 9x=3x+1.

Example 17

medium
A radioactive substance has a half-life of 10 years. If the initial amount is 200 g, how much remains after 30 years?

Example 18

medium
Identify the growth factor of g(x)=10⋅(1.25)x.

Example 19

medium
Solve 22x−5⋅2x+4=0.

Example 20

medium
Solve 4x=8.
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