The number of students that hear a rumor on a small college campus t days after the rumor starts is modeled by the logistic function r(t)= 3,000 1+bekt. if 5 students initially heard the rumor and 149 students heard the rumor after 1 day, then how long will it take 2,700 students to hear the rumor?

To solve this you need to find the unknown constants B and k.
The information given:
R(0) = 5
R(1) = 149
will allow us to do this.

First plug in initial point R(0) = 5 and solve for B  (e^0 = 1)



Next plug in R(1) = 149 and solve for k (actually only solve for e^k)


Finally we can solve for t when R(t) = 2700.
Plug in the fraction for e^k since e^(kt) = (e^k)^t