A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year.
Write an exponential function that models the value of the car, y, over x years.
To the nearest cent, what will be the value of the car after eight years?
y = 15250 * 0.925^x
To write an exponential function that models the value of the car over time, we can use the formula for exponential decay:
y = a(1 - r)^x
Where:
- y represents the value of the car after x years
- a represents the initial value of the car ($15,250 in this case)
- r represents the rate of decrease per year (7.5% or 0.075 as a decimal)
- x represents the number of years
Plugging in the given values, we have:
y = 15250(1 - 0.075)^x
To find the value of the car after eight years, we replace x with 8 and evaluate the function.
y = 15250(1 - 0.075)^8
Now we can calculate the value using a calculator or by simplifying the expression.
Using a calculator, we get:
y ≈ 7810.34
Therefore, to the nearest cent, the value of the car after eight years would be $7,810.34.