I have this problem that I really need somehelp with.
the rate of spread of a rumour is proportional to the product of the fraction y of 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