Practice Exponential Function in Math

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

Quick Recap

An exponential function has the form f(x) = a \cdot b^x where b > 0, b \neq 1. The variable is in the exponent, not the base.

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

Example 1

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

Example 2

medium
Solve 3^{2x - 1} = 81.

Example 3

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 4

hard
Two bacteria colonies start with 100 and 500 cells respectively. Colony A doubles every 3 hours; Colony B doubles every 8 hours. After how many hours will Colony A surpass Colony B?
← Back to Exponential Function Worked Examples Formula Explained