The exponential function that gives the value of the car in t years after 2008 is:
[tex]A(t) = 27500(0.88)^t[/tex].
Using the function, the estimate for the value of the car in 2016 is of $9,900.
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 initial value is of A(0) = 27,500.
- Considering the first year change, we have that 1 - r = 24200/27500 = 0.88.
Hence, the equation is:
[tex]A(t) = 27500(0.88)^t[/tex]
2016 is 8 years after 2008, hence the value of the car will be given by:
[tex]A(8) = 27500(0.88)^8 = 9900[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
