A spread of a rumor of free KFC chicken in the school lobby is modeled by the equation P(t)= (224)/(1+e^(5-t)), where P(t) is the total number of students who have heard t minutes after the deep-fried goodness has arrived.
a. Estimate the initial number of students who first heard about the giveaway of these finger-lickin' delights.
b. How fast is the rumor of sweet,tangy,belly-filling joy spreading after 4 minutes?
c. When is this rumor spreading at its maximum rate?
d. What is this rate?