A rumour starts that New Zealand is going to become part of Australia. The rate at which people hear the rumour is proportional to the number of people who have not heard the rumour. Let P be the population of New Zealand.

i) Write the differential equation which expresses this statement.

After 5 hours half the population have heard the rumour. Assume that no-one had heard the rumour at t = 0.

ii) solve the differential equation in part i) to find how long it would take for 90% of the population to have heard the rumour

Question

A rumour starts that New Zealand is going to become part of Australia. The rate at which people hear the rumour is proportional to the number of people who have not heard the rumour. Let P be the population of New Zealand.

i) Write the differential equation which expresses this statement. 

After 5 hours half the population have heard the rumour. Assume that no-one had heard the rumour at t = 0.

ii) solve the differential equation in part i) to find how long it would take for 90% of the population to have heard the rumour

anonymous · Answer

for part i) my answer is dN/dt = k(P-N)