Question

A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in years), of midsize luxury American automobiles. The equation of the line of best fit was determined below.
y = 181.7 - 20.21x
(a) Find the resale value in dollars of such a car when it is 3 years old. $_____(b) Find the resale value in dollars of such a car when it is 6 years old. $ _____(c) What is the average annual decrease in the resale price in dollars of these cars? $ _____

Answer 1

Answer:

a. $121.07

b. $60.9

C. $20.03

Step-by-step explanation:

From the equation given

Y=181.7-20.21x

Where y is in dollars and X is in years

a. To find the resale price after 3years we have, we substitute x=3 into the given equation.

We have

y=181.7-20.21(3)

y=181.7-60.63

y=121.07

The resale price after 3years is $121.07

b. To find the resale price after 6years we have, we substitute x=6 into the given equation.

We have

y=181.7-20.21(6)

y=181.7-120.72

y=60.98

The resale price after 3years is $60.98

C. To find the average decrease per year, we have

[(x=3)-(x=6)]/3

=(121.07-60.98)/3

$20.03

Hence the average annual decrease is $20.03

Answer 2

Answer:

a) y = 121.07 hundreds of dollars = $12,107

b) y = 60.44 hundreds of dollars = $6,044

c) Annual decrease is 20.21 hundreds of dollars

= $2,021

Step-by-step explanation:

Given:

y = 181.7 - 20.21x

Where;

y is the resale price in hundreds of dollars

x is the age in years.

a) Find the resale value in dollars of such a car when it is 3 years old.

x = 3

y = 181.7 - 20.21(3) = 181.7 - 60.63

y = 121.07 hundreds of dollars = $12,107

b) Find the resale value in dollars of such a car when it is 6 years old.

x = 6

y = 181.7 - 20.21(6) = 181.7 - 121.26

y = 60.44 hundreds of dollars = $6,044

c) What is the average annual decrease in the resale price in dollars of these cars?

The annual decrease is the slope of the equation

y = 181.7 - 20.21x

dy/dx = -20.21

Annual decrease is 20.21 hundreds of dollars

= $2,021