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

Answer:

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

Step-by-step 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:

$10\%=\frac{10}{100}=0.10$

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

Answer 2

y=20,000-.10x

with x being the number of years