"A rumour spreads through a population in such a way that t hours after its beginning, the percentage of people involved in passing the rumour is given by P(t) = 100(e^(-1) - e^(-4t)). What is the highest percentage of people involved in spreading the rumour within the first 3 h? When does this occur?"
Given the equation, P(t) = 100(e^(-1) - e^(-4t)), this is what I've done so far:
P(t) = 100(e^(-1) - e^(-4t))
P(t) = (100/e) - (100e^(-4t))
P'(t) = -100e^(-4t)(-4)
P'(t) = 400e^(-4t)
Where do I go from this point? If I make the equation equal to zero, I won't be able to solve for the time.
Thanks.