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3.) Your car cost $42,500 when you purchased it in 2015. The value of the car
decreases by 15% annually.
A. Write an exponential decay function to represent this situation.
f(x)=42500(1-.15)x
f(x)=42500(1-.85)x
B. How much will your car be worth in 7 years? Round your answer to the nearest
dollar.

Respuesta :

So, 42500 x .85 ^ 7 - 1

13623.52 is what i got

Using exponential function concepts, it is found that:

  • The model is: [tex]f(x) = 42500(0.85)^x[/tex].
  • The car will be worth $13,625 in 7 years.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem, the car initially cost $42,500, and the value decreases by 15% annually, hence A(0) = 42500, r = 0.15, and the model is given by:

[tex]f(x) = 42500(0.85)^x[/tex]

In 7 years, the values will be of:

[tex]f(7) = 42500(0.85)^7 = 13625[/tex]

More can be learned about exponential function concepts at https://brainly.com/question/25537936

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