Question

A parking lot charges $3 to park a car for the first hour and $2 per hour after that. If you use more than one parking space, the second and each subsequent car will be charged 75% of what you pay to park just one car. If you park 3 cars for t hours, which function gives the total parking charge?
A ) f(t) = 3(3 + 2(t − 1))

B ) f(t) = (3 + 2t) + 0.75 × 2(3 + 2t)

C ) f(t) = (3 + 2(t − 1)) + 0.75 × 2(3 + 2(t − 1))

D ) f(t) = (3 + 2t) + 0.75(3 + 2t) + 0.75 × 0.75(3 + 2t)

E ) f(t) = (3 + 2(t − 1)) + 0.75(3 + 2(t − 1)) + 0.75 × 0.75(3 + 2(t − 1))

Ps. I picked C

Answer 1

Consider the charge for parking one car for t hours.

If t is more than 1, then the function is y=3+2(t-1), because 3 $ are payed for the first hour, then for t-1 of the left hours, we pay 2 $.

If t is one, then the rule y=3+2(t-1) still calculates the charge of 3 $, because substituting t with one in the formula yields 3.


75% is 75/100 or 0.75. 

For whatever number of hours t, the charge for the first car is 3+2(t-1) $, and whatever that expression is, the price for the second car and third car will be 

0.75 times 3+2(t-1). Thus, the charge for the 3 cars is given by:

3+2(t-1)+0.75[3+2(t-1)]+0.75[3+2(t-1)]=3+2(t-1)+0.75 × 2[3 + 2(t − 1)].


Thus, the function which total parking charge of parking 3 cars for t hours is:

f(t) = (3 + 2(t − 1)) + 0.75 × 2(3 + 2(t − 1)) 


Answer: C