Estimate: The value of the car after 12 years is about $7000.
Practice makes perfect
a
We can model the value y of the car with an exponential decay function because the value of the car decreases by 9 % every year.
<premium partialsolution=1>y= a(1- r)^t
Here, a is the initial value of the car, r is the rate of decay, and t is the time in years. We know that the initial value of the car is $ 21 500, and the rate of decay is 9 %, or 0.09.
y= 21 500(1- 0.09)^t
⇓
y=21 500(0.91)^t
This function represents the value y of the car after t years when the initial value of the car is a.
