Determine the differential equation

Let N(t) be the fraction of the population who have heard a given piece of news t hours after its initial release.
According to one model, the rate of N'(t) at which the news spreads is equal to k times the fraction of the population that has not yet heard the news, for some constant K.

a) Determine the differential equation satisfied by N(t).
b) Find the solution of this differential equation with the initial condition N(0) = 0 in terms of k.

Fraction who have not heard the news = 1-N(t)
N'(t) = k[1-N(t)] = k - kN(t)