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Linear Growth vs. Exponential Growth

Question 1 • AZ-Common Core Algebra II B

Which of the following statements are true about the growth shown in the table?

Answer
A
The simple interest shows linear growth because it is adding a constant amount.
B
The simple interest shows exponential growth because it is adding a constant amount.
C
The compound interest shows linear growth because it is multiplying by a constant amount.
D
The compound interest shows exponential growth because it is multiplying by a constant amount.

Explanation

Simple interest adds the same amount each period, so its total increases by a constant difference and shows linear growth. Compound interest earns interest on the accumulated balance, so the balance is multiplied by the same growth factor each period and shows exponential growth. Thus, “adding a constant amount” describes linear growth, while “multiplying by a constant amount” describes exponential growth.

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