For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function f defined by f(t)=arctan(π2−t10). For time 5≤t≤10 , water is leaking from the tub at a rate given by the function l defined by l(t)=0. 03(20t−t2−75). Both f(t) and l(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by w(t).