Peicewise function

Question

First half hour = free

second half hour = $2.00

each additional half hr = $1.00

max daily rate = $24.00

write price wise function with at least one floor or ceiling function to model the cost of parking as a function of number of hours parked within a 24 hour span.

Answer 1

We will have to figure out after how many hours t the cost will reach the max daily rate.

f(t) = 2+ 1*2*(t-1) = 2*t = 24.

Solving for t, we get t = 12 hours. Thus, for t >= 12 hours, the price will be the max daily rate 24$.

Now that we have this information about the cost later on, we will write out the cost of parking in the first few hours. Thus, the piecewise function modeling the cost of parking as a function of the number of hours t is as follows:

f(t) = 0 $, if 0 <= t < 0.5

= 2 $, if 0.5 <= t < 1

= 2+ 2*(t-1) = 2*t $, if 1 <= t <12

= 24 $, if t >=12