V(t)=25,900(0.95^t) Word Problem

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)=25,900(0.95^t)

 

Find the initial value of the car and the value after 10 years.

Round answers to the nearest dollar as necessary.

 

Answer 1

V(t)=25,900(0.95^t)

 

The initial value occurs when t = 0:

 

     V(0) = V(t)=25,900(0.95⁰) = 25,900(1) = $25,900

 

After 10 years, t = 10:

 

     V(10) = 25,900(0.95¹⁰)

 

Use your calculator to compute the answer