Considering the definition of exponential function, the value of the car is 11,287.25 dollars.
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)= aˣ
Being a a positive real, a > 0, and different from 1, a ≠ 1.
When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.
In this case, the value of that car depreciates based on the function f(t)=12,000×[tex]0.96^{t}[/tex] where t is measured in years after purchase.
After 3/2 years, the value of the car is calculated as:
f(3/2)=12,000×[tex]0.96^{3/2}[/tex]
Solving:
f(3/2)= 11,287.25
Finally, the value of the car is 11,287.25 dollars.
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