Practice Growth vs Decay 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 multiplies by a factor > 1 repeatedly; exponential decay when it multiplies by a factor between 0 and 1.

Growth compounds: each period's increase is larger than the last. Decay shrinks: each period's decrease is smaller than the last, never quite reaching zero.

Example 1

easy
Classify each function as growth or decay, and find its value at x=3: (a) f(x)=4\cdot2^x, (b) g(x)=100\cdot(0.5)^x.

Example 2

medium
A radioactive substance has a half-life of 10 years. Starting with 200 g, write the decay function and find the amount remaining after 35 years.

Example 3

easy
A population grows by 8\% per year. Starting at 5000, write the growth function and find the population after 10 years.

Example 4

hard
Show algebraically that f(x)=e^{-0.3x} is an exponential decay function by rewriting it in the form a\cdot b^x and confirming 0<b<1.
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