Piecewise Functions

Question

A privately owned parking lot is open 12 hours each day. It charges a $5 fee to park plus $3/hr up to 4 hours and $2/hr after 4 hours and up to 12 hours. The charges are proportional. For example, if someone parked for 1/2 hour, they would be charged $6.50.

a. Determine the lot's revenue, R(t) (a piecewise function), for a car parked for t hours.

b. Use the revenue function you found in part (a) to determine the revenue from a car that is parked for 3 hours.

c. Use the revenue function you found in part (a) to determine the revenue from a car that is parked for 9 hours and 15 minutes.

Answer 1

R(t) = 5 + 3t, if 0 < t ≤ 4

= 2t, if 4 < t ≤ 12

R(3) = 5 + 3(3) = $14

R(9.25) = 2(9.25) = $18.50