Suppose 50 people have heard a rumour by 8am in a town of 3,000 people. Assume that the spread of the rumour follows the logistic equation,
dP/dt=kP(1-P/C).
(a) Given that 100 people have heard the rumour by 12 noon, determine how long it takes for half the population to have heard the rumour. Enter your answer in hours rounded to exactly one decimal place.
(b) How many people have heard it by 8pm? (Hint: You must round your answer down to get the appropriate integer.)