Question

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Answer 1

        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 ".

= $\dfrac{dp}{dt}$

"is proportional "

$\dfrac{dp}{dt} = k * \text{Unknown number}$

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

$p * (n-p)$

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