Hi, need help answering a question in a past exam paper. Below is the question:
5 mice in a stable population of 500 are intentionally infected with a disease. The rate of change in the infected population is proportional to the product of the number of mice who have the disease with the number that are disease free. If N(t) denotes the number of mice with the disease at time, t, the theory predicts that:
dN/dt = kN(500 - N)
where k is a constant. Show that the time taken for half the population to contract the disease is
I have substitued N=5 to give dN/dt = k x 5 x (495) but i dont understand what to do next.