Question

In 2013 your car was worth $12,500. In 2015 your car was worth $8,200.

A) Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2013.
B) Suppose the value of your car decreased exponentially. Write a function g to determine the value of your car (in dollars) in terms of the number of years t since 2013

Answer 1

A)
`V =12500[1-(17.2 * t)/(100) ]`

B)
`V = 12500[1-(19)/(100) ]^(t)`

Explanation:

In two years i.e. from 2013 to 2015 the car value decreases from $12500 to $8200.

a) If the rate of decrease is constant and it is r% per year, then

`8200 = 12500[1-(r * 2)/(100)}]`

⇒ r = 17.2%

Therefore, the value of the car is given by
`V =12500[1-(17.2 * t)/(100) ]`, where, t is in years since 2013. (Answer)

b) If the rate of decrease is exponential and it is r%, then

`8200 = 12500[1-(r)/(100) ]^(2)`

⇒ r = 19%

Therefore, the value of the car is given by
`V = 12500[1-(19)/(100) ]^(t)`, where, t is in years since 2013. (Answer)