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

Answer:

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

Step-by-step 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.

$12\%=\frac{12}{100}=0.12$

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.

Answer 2

ANSWER:

y= 12000*(0.88)x

Step-by-step 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.