Question

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

v (t) = 18,500 (0.84)^t
Find the initial value of the car and the value after 12 years.
Round your answers to the nearest dollar as necessary.
What’s the initial value ? Value after 12 years?

Answer 1

Answer: Initial Value is 18,500. Value after 12 years is about 2,283

Explanation:

The initial value assumes you have just bought the car, which means 0 years have passed. If zero is substituted as an exponent in ANY NUMBER, it equals 1. Therefore, the value is 18,500.

The value after 12 years can be found by substituting 12 in the space of t. Then, use a calculator to approximate the value of 0.84¹² which is equal to about 0.12. DO NOT ROUND, HOWEVER. Then, the previous value is multipled by 18,500, equalling about 2,283.