Question

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(pi/2-t/10). 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 -t^2-75). Both F(t) and L(t) are measured in cubic feet per minute, and t is meaured in minutes. The volume of water in the tub, at time t is given by W(t).

a. At t = 3 there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3, and use it to approximate the volume of water in the tub at t=3.5.

Answer 1