4.* Consider a population of fixed size K in which a rumor is being spread by word of mouth. Let y(t) be the number of people who have heard the rumor at time t and assume that everyone who has heard the rumor passes it on to r others in unit time. Thus, from time t to time (t+h). the rumor is passed on hry(t) times, but a fraction y(t)/K of the people who hear it have already heard it, and thus there are only hry(t) (****) people who hear the rumor for the first time. Use these assumptions to obtain an expression for y(t +h) - y(t), divide by h, and take the limit as h+ 0 to obtain a differential equation satisfied by y(t). 4.* Consider a population of fixed size K in which a rumor is being spread by word of mouth. Let y(t) be the number of people who have heard the rumor at time t and assume that everyone who has heard the rumor passes it on to r others in unit time. Thus, from time t to time (t+h). the rumor is passed on hry(t) times, but a fraction y(t)/K of the people who hear it have already heard it, and thus there are only hry(t) (****) people who hear the rumor for the first time. Use these assumptions to obtain an expression for y(t +h) - y(t), divide by h, and take the limit as h+ 0 to obtain a differential equation satisfied by y(t)