SAT Two-variable data: models and scatterplots Practice Question 4 (Hard)

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisHard

A used-car analyst modeled the value $y$ , in thousands of dollars, of a certain car model $x$ years after purchase with the exponential function $y = 28(0.85)^x$ . According to the model, by approximately what percent does the car's value decrease every $2$ years?

$15\%$

$28\%$

$30\%$

$72\%$

Show answer and explanation

Answer: B

Every year the value is multiplied by $0.85$ , so every $2$ years it is multiplied by $(0.85)^2 = 0.7225$ . The car keeps about $72.25\%$ of its value, so it loses about $100\% - 72.25\% = 27.75\%$ , or approximately $28\%$ .

Choice C doubles the yearly $15\%$ decrease, but percent decreases compound rather than add.

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