Hi everyone,

I have this problem that I really need somehelp with.

the rate of spread of a rumour is proportional to the product of the fractionyof the population L that has heard the rumour and the fraction who have not.

(1) Find the differential equation that is satisfied by y.

This is my answer

dy/dt = k * [y(L-y) / (L^2)]

(2) Show that the solution with initial condition y(0) = y0 is given by

y = (Ly0e^(kLt)) / ((L-y0)+y0e^(kLt))

I am lost on this.

(3) A school has 100 students. At 9am, 20 students have heard a rumour. At 11am 50 students have heard the rumour. At what time will 80 students will have heard the rumour.

I dont know what to do here either, however, im guessing these are the initial conditions. i.e.

y(0) = 20

y(2) = 50

Please help me