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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.

Respuesta :

sqdancefan

Answer:

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

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

Step-by-step 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

serenityo90

Answer:

A) car one is linear because it decreases the same amount every year.  

    car two decreases by the same ratio so it's exponential.  

B) for car one y = -6,000x + 38,000 (y is the value after x years, -6,000 is what it changes by every year, and 38,000 is the amount of year 0)

   for car two y = (44,000) (17/20)x-1 (y is the value after x years, 44,000 is the amount on year 0, and 17/20 is the ratio)

C) after 5 years car one will be 8,000

    after 5 years car two will be about 16,860

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