The Xylocom Company has 1000 employees. On Monday a rumor began to spread among them that the CEO had suddenly moved to Brazil. Let y=y(t) be number of employees who have heard the rumor after t days (i. e. t=0 corresponds to midnight at the beginning of Monday). It is reasonable to assume that the rate of the spread of the rumor is proportional to the number of encounters between employees who have heard the rumor and those who have not. The above statement means that the rate of change of the number of employees who have heard the rumor (i. e. dy dt ) is proportional to the product of the number of people who have heard the rumor (y) times the number of people who haven't (1000−y). Use this to write down a differential equation that describes this model of the spread of a rumor.