The exponential equation that represents the value of the car is [tex]A = 15000(1.08)^t[/tex].
Depreciation is the rate by which the value of an object reduces with respect to time. it is given by the formula,
[tex]A = P(1-\dfrac{r}{100})^t[/tex]
where A is the value of object after t period of time, P is the principal amount, r is the rate of depreciation, and t is the time period.
We know the formula of the depreciation, Also, the initial value of the car is $15,000, and the rate of depreciation r that is 8% per year. Therefore, the function of the depreciation of the car can be written as,
[tex]A = P(1-\dfrac{r}{100})^t\\\\A = 15000(1-\dfrac{8}{100})^t\\\\A = 15000(1.08)^t[/tex]
Hence, the exponential equation that represents the value of the car is [tex]A = 15000(1.08)^t[/tex].
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