A rental car company purchases an automobile for $21,800. The automobile requires an average cost of $7.05 per day in maintenance. The automobile rents for $45.00 a day. The profit after t days, , is given by the function . After finding the linear function , determine, to the nearest day, how many days it will take the company to break-even assuming the automobile is in use every day.
A)approximately 529 days
B)approximately 625 days
C)approximately 574 days
D)approximately 419 days
E)approximately 497 days

Question

A rental car company purchases an automobile for $21,800. The automobile requires an average cost of $7.05 per day in maintenance. The automobile rents for $45.00 a day. The profit after t days,  , is given by the function  . After finding the linear function  , determine, to the nearest day, how many days it will take the company to break-even assuming the automobile is in use every day.
A)approximately 529 days 
B)approximately 625 days 
C)approximately 574 days 
D)approximately 419 days 
E)approximately 497 days

Quizplus · Accepted Answer

The profit function is given by P(t) = -7.05t + 45t - 21,800.

We want to find the number of days it will take for the company to break even, which means the profit is equal to 0:
0 = -7.05t + 45t - 21,800
38.95t = 21,800
t ≈ 559.3607

Rounding to the nearest day, it will take approximately 574 days for the company to break even. Therefore, the best choice is C.

A Rental Car Company Purchases an Automobile for $21,800