Question

Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. What is the decay factor for the value of the car? Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. What is the decay factor for the value of the car? Use your equation to determine the value of the car six years after Kelly purchased it.

Answer 1

Decay factor is 0.9,

The value of the car after 6 years is $10,628.82.

Explanation:

Given,

The original value of the car, P = $20,000,

Also, the annual decreasing rate, r = 10 %,

So, the value of the car after t years,

`A=P(1-(10)/(100))^t`

`=20000(1-0.1)^t`

`=20000(0.9)^t-----(1)`

Now, a function
`f(x) =ab^x` is called exponential function,

Where, a and b are any constant,

There are two type of exponential function,

Decay : If 0 < b < 1, where b is called decay factor,

Growth : If b > 1, where b is called growth factor,

By comparing,

Decay factor of the function (1) is 0.9,

If t = 6,

Then the value of the car after 6 years would be,

`A=20000(0.9)^6=\$10628.82`