Question

A new car is purchased for 18,000 dollars. The value of the car depreciates at 11.5% per year. What will the value of the car be, to the nearest cent, after 10 years?

Answer 1

Explanation:

The exponential decay function is

`v(t)=a(b)^t` where b, the rate of decay, for us is (1 - .115) and a is the original value of the car which, for us, is 18000. t is the time in years. Using this information to write the equation we need to solve for the value when the car is 10 years old:

`v(t)=18000(.885)^t` and we sub in 10 for t:

`v(t)=18000(.885)^{10` which simplifies to

v(t) = 18000(.2947356754) so

v(t) = 5305.24