Question

Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. Write an equation to model the car's value.

Answer 1

y=20,000-.10x

with x being the number of years

Answer 2

`y=\$20,000\cdot (0.90)^x`

Explanation:

We have been given that Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year. We are asked to write an equation to model the car's value.

Since car's value depreciates by 10% per year, so value of car is depreciating exponentially.

We know that an exponential decay function is in form
`y=a\cdot (1-r)^x`, where

a = Initial value,

r = Decay rate in decimal form.

Let us convert 10% into decimal form as:

`10\%=(10)/(100)=0.10`

Upon substituting our given values in decay formula, we will get:

`y=\$20,000\cdot (1-0.10)^x`

`y=\$20,000\cdot (0.90)^x`

Therefore, our required equation would be
`y=\$20,000\cdot (0.90)^x`.