Question

A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be, to the nearest cent, after 11 years?

Answer 1

The starting value is 20,300, and the value is decreasing by 9.5% each year.

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.

A decrease by 9.5% corresponds to multiplying by 91.5% each year.

We write . We plug in 11 years for t.

$A(t)=23000(0.915)^{t}\\\\A(11)=23000(0.915)^{11}\\\\A(11)=7671.18$

$7,671.18