Question 1143109: Below is data for two models of a certain car, assume gas is
$per gallon.
Base Price ($) Cost/Mile ($)
Hybrid $22,000 $0.11
Standard $18,000 $0.14
a. Find the cost function for each car, as a function of miles driven x.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! price of first car is $22,000 + .11 per mile.
price of second car is $18,000 plus .14 per mile.
let x = the number of miles driven.
cost function for first car if f(x) = 22,000 + .11 * x.
cost function for second car is f(x) = 18,000 + .14 * x.
if these are the only considerations, then the total cost for the cars will break even when the cost function for the first car is equal to the cost function for the second car.
you get 22,000 + .11 * x = 18,000 + .14 * x
subtract 18,000 from both sides of the equation and subtract .11 * x from both sides of the equation to get:
4,000 = .03 * x
solve for x to get x = 4,000 / .03 = 133,333.3333.
the total cost for the cars would be the same after they have both traveled 133,333.3333 miles.
total cost for first car becomes 22,000 + .11 * 133,333.3333 = 36,666.66667.
total cost for second car becomes 18,000 + .14 * 133,333.3333 = 36,666.6667.
your solution is that the cost function for the first car is f(x) = 22,000 + .11 * x and the cost function for the second car is f(x) = 18,000 + .14 * x.
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