SOLUTION: Bobbi bought a used car for $7,200. The car’s value decreases at a constant rate each year. After 9 years, the value decreased to $3,600 Use a function to model the car’s valu

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Bobbi bought a used car for $7,200. The car’s value decreases at a constant rate each year. After 9 years, the value decreased to $3,600 Use a function to model the car’s valu      Log On


   

Question 1151692: Bobbi bought a used car for $7,200. The car’s value decreases at a constant rate each year. After 9 years, the value decreased to $3,600
Use a function to model the car’s value as the number of years increases. Find this function’s domain and range in this context.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
When x=0 years have passed the value is y=$7200.
When x=9 years have passed the value is y=$3600.

So we want the equation of a line that goes through the points
(0,7200) and (9,3600)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%283600-7200%29%2F%289-0%29

m=%28-3600%29%2F9

m=-400

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-7200=-400%28x-0%29

y-7200=-400x

y=-400x%2B7200

or

f%28x%29=-400x%2B7200

The smallest value of x in the domain is when the largest value y is the full 
value of $7200.  That's when x=0 years.

The least value of x in the domain is when the smallest value is $0, when it is 
worthless.  We have to calculate that by substituting 0 for y and solving for x.

0=-400x%2B7200
-400x=-7200
%28-400x%29%2F%28-400%29=%28-7200%29%2F%28-400%29
x=18

So the domain is [0,18]  (years)

The range is [0,7200]  (dollars)

Edwin