SAT Math · Nonlinear functions · easy

A car's value, in dollars, after t years is modeled by V(t) = 28,000(0.82)^t. By what percent does the car's value decrease each year?

A car's value, in dollars, after tt years is modeled by V(t)=28,000(0.82)tV(t) = 28{,}000(0.82)^t. By what percent does the car's value decrease each year?

Answer and explanation

Answer: 18

In an exponential model V(t)=V0btV(t) = V_0 b^t, the base bb is the yearly multiplier. Here b=0.82=1−0.18b = 0.82 = 1 - 0.18, so the car keeps 82% of its value each year and loses 18%. The answer is 18. A common wrong answer is 82, which is the percent that remains rather than the percent lost. Another is 0.82, which misreads the decimal as a percent. A third is 28,000, the starting value. For decay, subtract the base from 1 and convert the result to a percent.

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