Question

A vessel is being filled at a variable and the volume of liquid in the vessel at any time t is given by V = A( 1- e^-kt) V

a) Show that dV/dt = k(A-V)

b) if one quarter of the vessel is filled in 5 minutes, what fraction is filled in the next 5 minutes?

c) show that lim (x-> infinite) = A.


Thank you!