Question

Cindy is buying a new car and wants to learn how the value of her car will change over time. Insurance actuaries predict the future value of cars using depreciation functions. One such function is applied to the car whose declining value is shown at the right. Write an exponential function for it.

Answer 1

`C=10000(0.852)^t`

Explanation:

Let the exponential function be,

`C=a(b)^t`

Here, C = cost of the car

t = Duration or period in years

From the given table,

Two points representing cost of the car and time are (10000, 0) and (8520, 1),

For (10000, 0),

`10000=a(b)^0`

a = 10000

For (8520, 1)

8520 =
`10000(b)^1`

`b=(8520)/(10000)`

b = 0.8520

Therefore, exponential equation will be,

`C=10000(0.852)^t`