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.
