What is the piecewice function to model the situation?

Question

The community park has a small lake where visitors can rent paddle boats at $1 for 15 minutes, up to 2 hours. After 2 hours, the rate increases to $3 for 30 min

Answer 1

f(x) = price, x = time

 

In minutes,

 

f(x) = x(1/15) ;  0 <= x <= 120

      = 8 + (x-120)*(3/30) ; x >= 120

 

In hours,

 

f(x) = x(4/1) ; 0 <= x <= 2

      = 8 + (x-2)*(6/1) ; x >= 2

Either is the answer depending on what unit do you wanna use. I put the fraction forms so that you can easily see that those are the rates.