Liquid is pouring into a container at a constant rate of 20 cm 3s-1 and is leaking out at a rate proportional to the volume of the liquid already in the container.
(a) explain why, at time t seconds, the volume, V cm3 of liquid in the container satisfies the differential equation dv / dt = 20 - kV, where k is a positive constant.
The container is initially empty.
(b) by solving the differential equation, show that V= A + Be-kt, giving the values of A and B in terms of k.
So given that dv / dt = 10 when t = 5
(c) find the volume of liquid in the container at 10s after the start.
(p.s.i have attached a document with my own answers)