The cost of the plan is $15.00 for the first 60 minutes. Each additional minute (or portion of a minute) costs $0.50, then if you use 61 minutes, it is 1 additional minute, then the charge will be $15.00+$0.50*1=$15.50.
When you use 2 additional minutes, the charge will be $15.00+$0.50*2=$16.00.
And when you use 3 additional minutes, the charge will be $15.00+$0.50*3=$16.50.
Then, the function after 60 minutes depends on the additional minutes you used. Let's call it t. It can be represented by 15.00+0.50*t. Therefore:
[tex]f(t)=\begin{cases}15.00\text{ 0}\leq t\leq60 \\ 15.00+0.50t\text{ 60}