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Sagot :
Using an exponential function, it is found that the equation that represents the value of the car after 5 years is:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
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 is purchased for 21,800 dollars, and it's value deprecites 9.5% per year, hence the equation for it's value after t years is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 21800(1 - 0.095)^t[/tex]
[tex]A(t) = 21800(0.905)^t[/tex]
After 5 years, the value is given by:
[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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