Question

Topic: Modeling exponential functions

Kathy plans to purchase a car that depreciates
(loses value) at a rate of 14% per year. The initial
cost of the car is $21,000. Which equation
represents the value, v, of the car after 3 years?
1) v = 21,000(0.14)
2) v = 21,000(0.86)
3) v= 21,000(1.14)
4) v= 21,000(0.86)(3)

Answer 1

Explanation:

The standard form equation for this type of problem is

`y=a(b)^x` where a is the initial value, b is the rate of depreciation, and x is the number of years in question. Because the value of the car is going down, b can also be written as (1 - r) where r is the rate of depreciation. For us, then, the equation will look like this:

`y=a(1-r)^x` and filling in:

`y=21000(1-.14)^3` which in simplified form is

`y=21000(.86)^3` which I'm assuming is how choice 4 should look.