An SUV is purchased new for $$ 31, 500$ .
Part 1 of 4
(a) Write a linear function of the form $y = m t + b$ to represent the value $y$ of the vehicle $t$ years after purchase. Assume that the vehicle is depreciated by $$ 3150$ per year.
The model for the value of the car $t$ years after purchase is $y = - 3150 t + 31500$ .
Alternate Answer:
$y = - 3150 t + 31, 500$
Part 2 of 4
(b) Suppose that the vehicle is depreciated so that it holds only $90 %$ of its value from the previous year. Write an exponential function of the form $y = V_{0} b^{t}$ , where $V_{0}$ is the initial value and $t$ is the number of years after purchase.
The model for the value of the vehicle $t$ years after purchase is $y = 31500 (.90)^{t}$
Alternate Answer:
$y = 31, 500 (0.9)^{t}$
Part: $2 / 4$
Part 3 of 4
(c) To the nearest dollar, determine the value of the vehicle after $5 yr$ and after $10 yr$ using the linear model. According to the linear model, the vehicle will be worth $$ ◻$ after 5 years, and $$ ◻$ after 10 years,

Answer

Expert–verified

Hide Steps

Answer

$According to the linear model, the vehicle will be worth 15750 a f t e r 5 y e a r s, a n d 0 after 10 years.$

Steps

Step 1 ：The linear function to represent the value of the vehicle t years after purchase, assuming that the vehicle is depreciated by $3150 per year, is given by $y = - 3150 t + 31500$ .

Step 2 ：The exponential function to represent the value of the vehicle t years after purchase, assuming that the vehicle holds only 90% of its value from the previous year, is given by $y = 31500 (0.9)^{t}$ .

Step 3 ：To find the value of the vehicle after 5 years and 10 years using the linear model, we substitute t=5 and t=10 into the linear model $y = - 3150 t + 31500$ .

Step 4 ：Substituting t=5 into the linear model gives a value of $15750 for the vehicle after 5 years.

Step 5 ：Substituting t=10 into the linear model gives a value of $0 for the vehicle after 10 years.

Step 6 ： $According to the linear model, the vehicle will be worth 15750 a f t e r 5 y e a r s, a n d 0 after 10 years.$

Answer

Popular Problems