Practice Exponential Growth in Math

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

Quick Recap

Exponential growth occurs when a quantity increases by a constant multiplicative factor over equal intervals.

Exponential growth means the amount added each period is proportional to the current amount — the bigger it gets, the faster it grows, creating an accelerating curve.

Example 1

easy
A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours?

Example 2

medium
A city's population grows at 3\% per year. If the current population is 200{,}000, when will it reach 300{,}000?

Example 3

medium
An investment grows from \1{,}000 to \1{,}500 in 5 years with continuous compounding. Find the annual growth rate.

Example 4

hard
Two populations grow exponentially: P_1(t) = 100 \cdot 3^t and P_2(t) = 5000 \cdot (1.2)^t. When will P_1 overtake P_2?
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