number of people who hear a rumor after t hours is
N(t) = 2000/ 1 + 499e^-0.3t
How long will it take for 200 people to hear the rumor?
I believe you are missing parentheses in the expression. In any case, the solution for t is the answer.
Solve for t in
N(t) = 200 = 2000/ (1 + 499e^-0.3t)
I get t=0.0243 (hour)