How do logistic and exponential growth differ?
Logistic is limited growth, and exponential is unbounded growth.
If the number of people, y, who have heard a rumor is growing at a rate proportional to how many have heard it, then we get the differential equation y' = ky, where y' = dy/dt. In this case the growth is exponential, and the solution is y = A
Examples of exponential growth are compound interest and bacteria growth, assuming an infinite amount of money or fuel.
But there are finitely many people B in the world, currently B =
Logistic growth is seen in "learning curves", internet popularity, and (did you hear) rumors! - - - \dansmath strikes again/