Question

A new car is purchased for $32,500. The car depreciates every year ata

rate of 14%. Write an exponential function that represents that situation

Answer 1

`y=32500(0.86)^(x)`

Explanation:

General exponentially depreciating function is given as

`y= a(1-b)^(x)`------------(1)

Where a is initial value, b is percent depreciation/unit time and x is time

Here

`a=32,500 \ \ \ b=0.14 \ \ \ and \ \ x \ is \ time \ in \ years`

Substituting above values in equation (1)

`y=32500(0.86)^(x)`

At x=0

`y=32500(0.86)^(0)\\y=32500`

At x=1

`y=32500(0.86)^(1) \\y=27950`