Question

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.

v(t) = 32,000(0.95)^t

Find the initial value of the car and the value after 13 years.
Round your answers to the nearest dollar as necessary.

Answer 1

v(0) = 32,000 . . . dollars

v(13) = 16,427 . . . dollars

Explanation:

The initial value is the value of the function for t=0. Put that into the formula and evaluate.

v(0) = 32,000(0.95^0) = 32,000 . . . . dollars

__

The value after 13 years is the function value for t=13. Put that into the formula and evaluate.

v(13) = 32,000(0.95^13) ≈ 32,000·0.513342 ≈ 16,427 . . . . dollars