SOLUTION: A used car has a value of $15,250 when it is purchased in 2012. The value of the car depreciates at a rate of 7.5% per year. Write an exponential function that models the value

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A used car has a value of $15,250 when it is purchased in 2012. The value of the car depreciates at a rate of 7.5% per year. Write an exponential function that models the value       Log On


   

Question 933535: A used car has a value of $15,250 when it is purchased in 2012. The value of the car depreciates 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?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
y = 15250 * (1-.075)^x

this simplifies to y = 15250 * .925^x

when x = 8, the value of the car is equal to 15250 * .925^8 = 8173.42

each year it's worth 7.5% less.

example:

in year 7 it was worth 8836.13

7.5% of 8836.13 = 662.71

subtract that from 8836.13 and you get 8173.42.

this happens every year.

the graph of the equation looks like this:

the horizontal line is at y = 8173 which intersects the graph of the equation in year 8.

graph%28600%2C600%2C-1%2C10%2C-1000%2C20000%2C15250%2A.925%5Ex%2C8173%29