Efficient Car Problem

Question

A particular brand of car with the normal engine cost $11000 to purchase, and 22 cents a mile to drive. The same car with a fuel-injection engine cost 11300 to purchase, but only 20 cents a mile to operate. 

a) Let d be a variable equal to the number of miles you have driven the car, let f(d) be the total number of dollars it cost to own the 11,000$ care. Write a particular equation for the function f. 

b) calculate f(1,000), f(10,000), f(100,000)

c)Let g(d) be the total number of dollars it cost to drive the $11,300 car. Write a particular equation for the function g.

d)Calculate g(1,000), g(10,000), and g(100,000)

e) How many miles would you have to drive to "break even"? The is, when does the total coast of owning the car with the normal engine equal the cost of owning the car with the fuel-injected engine?

AND SHOW ALL WORK

Answer 1

a) f(d)=$11,000+$0.22d

b) f(1000)=$11,000+$0.22(1000)

    f(1000)=$11,000+$220

    f(1000)=$11,220

    You can do the others !

c) Write the equation just like part a).

d) This is done just like part b).

e) $11,000+$0.22d=$11,300+$0.20d

    $0.22d-$0.20d=$11,300-$11,000

    0.02d=300

         2d=30,000

           d=30,000/2

           d=15,000 miles to break even (and the cost of ownership of each car would be $14,300)