Answer: Initial value of car = $ 27500
And, the value of car after 13 years is $5219.242
Step-by-step explanation:
Here, the given function that models the price of car after t years,
![v(t) = 27500(0.88)^t](https://tex.z-dn.net/?f=v%28t%29%20%3D%2027500%280.88%29%5Et)
Since, initially, t = 0
Thus, the initial value of the car,
![v(0) = 27500(0.88)^0=27500](https://tex.z-dn.net/?f=v%280%29%20%3D%2027500%280.88%29%5E0%3D27500)
Now, after 13 years, t = 13
Thus, the value of car after 13 years,
![v(13)=27500(0.88)^{13}](https://tex.z-dn.net/?f=v%2813%29%3D27500%280.88%29%5E%7B13%7D)
= ![27500\times 0.189790617123](https://tex.z-dn.net/?f=27500%5Ctimes%200.189790617123)
= ![5219.24197088\approx 5219.242](https://tex.z-dn.net/?f=5219.24197088%5Capprox%205219.242)