12
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Linear Growth vs. Exponential Growth

Question 12 • AZ-Common Core Algebra II B

Which of the following situations describe exponential growth? Check all of the boxes that apply.

Answer
A
The number of butterflies in an area increases by 10% per year.
B
The population of a city increases by 500 people per year.
C
Kristy bought a collector’s coin for $2.15 and its value increases at a rate of 3% per year.
D
The number of people who have heard a rumor increases because every person tells 2 other people.

Explanation

Exponential growth happens when an amount increases by a constant percentage or is multiplied by the same factor over equal intervals. The butterflies grow by 10% each year, and the coin’s value grows by 3% each year, so A and C are exponential. In D, each person tells two others, causing the number reached to multiply over time. The city’s population in B grows by a fixed 500 people per year, which is linear growth.

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