SAT Two-variable data: models and scatterplots Practice Question 9 (Hard) | SAT Owl

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisHard

The number of subscribers $y$ , in thousands, to a streaming service $x$ years after $2010$ can be modeled by an exponential function of the form $y = ab^x$ , where $a$ and $b$ are positive constants. The model estimates $400$ thousand subscribers in $2012$ and $1{,}350$ thousand subscribers in $2015$ . According to the model, by what percent does the number of subscribers increase each year?

A

$35\%$

B

$50\%$

C

$150\%$

D

$237.5\%$

Show answer and explanation

Answer: B

From $2012$ to $2015$ is $3$ years, so $b^3 = \frac{1350}{400} = 3.375$ . Taking the cube root, $b = 1.5$ . A growth factor of $1.5$ means the number of subscribers increases by $50\%$ each year.

Choice D is the total percent increase over the three years ( $3.375 - 1 = 2.375$ ), not the yearly increase.

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