A cell phone company charges $15 for the first 60 minutes or less used in a month and $0.50 for each additional minute or portion of a minute. Create a piecewise function that shows the charges for time t where t ranges from 0 to 63 minutes.
Let C(t) be the charges for time t in minutes.
For t ≤ 60, the charges are a flat rate of $15, so the function is:
C(t) = $15
For t > 60, the base charge is $15 for the first 60 minutes, and then an additional charge of $0.50 for each additional minute or portion of a minute. So, the function is:
C(t) = $15 + ($0.50)(t - 60)
Combining both cases, the piecewise function that represents the charges for time t (in minutes) is:
C(t) = $15 if t ≤ 60
$15 + ($0.50)(t - 60) if t > 60