Chapter 16.5, Problem 58E

Spread of a Rumor Suppose the rate at which a rumor spreads—that is, the number of people who have heard the rumor over a period of time—increases with the number of people who have heard it. If y is the number of people who have heard the rumor, then

$\frac{dy}{dt}=ky,$

  where t is the time in days.

1. (a) If y is 1 when t = 0, and y is 5 when t = 2, find k.

  Using the value of k from part (a), find y for each time.

  (b) t = 3    (c) t = 5    (d) t = 10