Question

David bought a used Dodge Challenger for $14,000. The value of the car depreciates 11% per year from the time he bought the car. Write a function that represents the value of David’s car, V(t), after t years. B) graph a function that represents the value of David’s car, V(t), after t yearsC) how much will David’s car be worth 6 years after he bought it?

Answer 1

EXPLANATION

Challenger cost = $14,000

Car depreciaton = 11%/yr = 0.11 (in decimal form)

A) The function that represents the value of David's car V(t) is the following:

`y=a(1-r)^t`

Where y= value as a function of t, a= initial amount and r is the rate of depreciation.

Replacing terms:

`V(t)=14,000(1-0.11)^t`

B) Now, we can graph the function by drawing some points:

C) The car's value after 6 year would be given by pluggin in t=6 into the function:

`V(6)=14000(1-0.11)^6`

Computing the power:

`V_((6))=14,000(0.89)^6=14,000\cdot0.496=6957`

The value of the car after 6 years would be $6957.