Do you mean to divide?
N(t) = 650/(1+649e^-.5t)
What's the trouble? Straightforward evaluation of N or solving for t. That's just algebra.
If I have the function right, its graphs is
http://www.wolframalpha.com/input/?i=650%2F%281%2B649e^%28-.5t%29%29
N(t) = 650
1+649 e−0.5 t
.
(You may wish to sketch a graph of N(t) to help you understand this situation and answer the questions below.)
(a) How many people will have heard the rumor after 2 hours?
After 12 hours?
(b) When will half the people have heard the rumor? t =
(c) When is the rumor spreading fastest? t =
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