The number of users of an app t months after launch is modeled by N(t) = 2,400(1.2)^t3. According to the model, by what percent does the number of users increase every 6 months?

SAT Nonlinear functions Practice Question 19 (Hard)

Math · Advanced MathHard

The number of users of an app $t$ months after launch is modeled by $N(t) = 2{,}400(1.2)^{\frac{t}{3}}$ . According to the model, by what percent does the number of users increase every $6$ months?

$20\%$

$40\%$

$44\%$

$120\%$

Show answer and explanation

Answer: C

Every 3 months, $N$ is multiplied by $1.2$ . Six months contains two 3-month periods, so $N$ is multiplied by $(1.2)^2 = 1.44$ . A factor of $1.44$ is a $44\%$ increase.

Choice B doubles the $20\%$ rate, but percent growth compounds rather than adds.

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