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 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 ".
= [tex] \dfrac{dp}{dt} [/tex]
"is proportional "
[tex]\dfrac{dp}{dt} = k * \text{Unknown number}[/tex]
"product of number of people who heard rumor and who haven't"
[tex]p * (n-p)
[/tex]
Since n is the total population the correct answer is (b).
