Help with Derivatives in Word Problems

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?