(e) The number of germs in a petri dish t hours after the start of observations is denoted by N. The variation in the number of germs is modelled by the differential equation dN = kN, where k is a constant and N is taken to be a continuous variable measured in millions. dt It is given that N = 50 when t = 0. Given also that N = 100 when t = 10, find how many hours pass before the number of germs in the petri dish has N exceeding 1000. Give the results of any integration needed to solve this problem.