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Exponential relationships — ACT practice questions

Practice 48 Exponential relationships questions in the app

What this topic is

Exponential relationships on the ACT Mathematics test cover equations and models in which a quantity grows or decays by a constant factor.

Students should rewrite expressions with a common base to solve for an unknown exponent, read a growth factor as an annual percent change, and apply repeated doubling or similar scaling over equal time intervals. Questions typically appear as multiple-choice items with five options, often algebraic equations, formula interpretations, or short word problems about an account or quantity.

Common traps include treating the growth factor as the percent itself, miscounting how many doubling periods fit in a given span, and applying linear rather than multiplicative change.

Sample questions

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Question 1Easier

Derek invests 350 dollars in an account whose balance doubles every 7 years. If no money is added or withdrawn, what is the balance after 21 years?

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Answer: A — 2,800

Twenty-one years contains 3 doubling intervals. The balance is 350(2)3=2,800350(2)^3=2{,}800 dollars.

Question 2Mid

What is the value of xx that satisfies 8x−1=4x+28^{x-1}=4^{x+2}?

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Answer: D — 7

Rewriting gives 23x−3=22x+42^{3x-3}=2^{2x+4}. Equating exponents, 3x−3=2x+43x-3=2x+4, yields x=7x=7.

Question 3Easier

A quantity is modeled by C(t)=4,200(1.06)tC(t)=4{,}200(1.06)^t, where tt is the number of years. Which of the following describes the annual percent change in the quantity?

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Answer: B — 6%6\% increase

The growth factor 1.06 equals 1+0.061+0.06. Therefore, the model represents approximately a 6%6\% increase each year.

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Practice 48 Exponential relationships questions in the app

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