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**huntelaar2011** 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 do have my own answers but wanted to see if a different calculation is given by others, i can post my answers up on this thread if others want to see my own work).