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You recently bought a new car and are curious how much it’s value drops over time. You do some research and find out that your brand of car depreciates 10% per year and you bought it new for $12,000. Write an exponential equation to represent the value of the car, f(x), based on the number of years since you bought it (x) (show work)

A) how much will your car be worth after 5 years?

B) how much will your car be worth after 12 years?

Respuesta :

The exponential equation that represents the value of the car after x years is given by:

[tex]f(x) = 12000(0.9)^x[/tex]

Using the equation, it is found that:

a) After 5 years, the car will be worth $7,086.

b) After 12 years, the car will be worth $3,389.

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 depreciates 10% per year, hence [tex]r = 0.1[/tex].
  • You bought it new for $12,000, hence [tex]A(0) = 12000[/tex].

Then, the function is:

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

[tex]A(t) = 12000(1 - 0.1)^t[/tex]

[tex]f(x) = 12000(0.9)^x[/tex]

Item a:

After 5 years, the value of the car is of f(5), hence:

[tex]f(5) = 12000(0.9)^5 = 7086[/tex]

Item b:

After 12 years, the value of the car is of f(12), hence:

[tex]f(12) = 12000(0.9)^{12} = 3389[/tex]

You can learn more about exponential equations at https://brainly.com/question/25537936

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