Question

Jason estimates that his car loses 12% of its value every year. The initial value is $12,000. Which best describes the graph of the function that represents the value of the car after x years?

Answer 1

y= 12000*(0.88)x

Explanation:

We have been given that Jason estimates that his car loses 12% o

Since the value of car is decreasing exponentially, so we will use exponential decay function to find the graph that represents the value of the car after x years.

Answer 2

`y=12,000*(0.88)^x`

Explanation:

Please find the attachment.

We have been given that Jason estimates that his car loses 12% of its value every year. The initial value is $12,000.

Since the value of car is decreasing exponentially, so we will use exponential decay function to find the graph that represents the value of the car after x years.

An exponential decay function is in form:
`y=a*(1-r)^x`, where,

a = Initial value,

r = Decay rate in decimal form.

Let us convert our given rate in decimal form.

`12\%=(12)/(100)=0.12`

Upon substituting our given values in decay function we will get,

`y=12,000*(1-0.12)^x`

`y=12,000*(0.88)^x`

We can see from our graph that as x approaches infinity, y approaches to zero, therefore, our graph will have a horizontal asymptote at y=0.

Therefore, the function
`y=12,000*(0.88)^x` represents the value of the car after x years.