What is the initial value of the car and the value after 13 years?

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)=26,000(0.84)^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

This is an exponential function.

Y intercept (when x = 0) is another name for the initial value. Plug in x=0, and the initial value is 26,000.

This variable, right before the (), is known as A, and is the initial value in an exponential function.

T in the function is in years, so plug in 13 for T.

v(t)=26,000(0.84)¹³ = v(t)=26,000* 0.1036 = $2695.28

This makes sense because .84 in the () is actually 1-.1 or in englush value of the car decreases by 16 percent each year.

Hope this helps!

Answer 2

Hey Stefani,

I answered another one of your questions here:

https://www.wyzant.com/resources/answers/837742/if-the-rate-of-inflation-is-2-5-per-year-the-future-price-p-t-in-dollars-of

This question is nearly identical in process. To find the initial price, you'll want to use t=0. To find the price 13 years from now, use t=13.

Hope this helps!