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))

Answer 1

Given, a parking lot charges $3 for first hour and $2 per hour after that.

So for t hours, the parking lot charges $3 for the first hour and after first hour there is
`(t-1)` hours left.

So for
`(t-1)` hours it will charge $2 per hour.

The charges for
`(t-1)` hours = $
`2(t-1)`.

Total charges for t hours for one car = $
`(3+2(t-1))`

Now for the second car, it will charge 75% of the first car.

So the charges for second car

=$[
`(3+2(t-1))(75/100)`]

=$
`0.75(3+2(t-1))`

There are 3 cars. That parking charges for the third car is also 75% of the first car.

So for third car the parking charges are same as for the second car.

Total parking charges for 3 cars

= $
`(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))`

We have got the required answer here.

The correct option is option C.