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question:
"a rumor spreads among a population of n people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor. if p denotes the number of people who have heard the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant? "

a.

b.

c.

d.

e.

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        A rumor spreads among a population of [unknown number] people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor.

        If [variable] p denotes the number of people who have heard the rumor, the differential equations could be used to model the situation with respect to time (t), where as (k) is a positive constant. 

As stated : "a rumor is changing at a rate ".

=

"is proportional "



"product of number of people who heard rumor and who haven't"



Since n is the total population the correct answer is (b).