apologiabiology
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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. [tex] \frac{dp}{dt}=kp [/tex]

B. [tex] \frac{dp}{dt}=kp(N-p)[/tex]

C. [tex] \frac{dp}{dt}=kp(p-N)[/tex]

D. [tex] \frac{dp}{dt}=kt(N-t)[/tex]

E. [tex] \frac{dp}{dt}=kt(t-N)[/tex]

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Respuesta :

Β  Β  Β  Β  A rumor spreads among a population of [unknown number]Β 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.

Β  Β  Β  Β  If [variable]Β 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.Β 

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).Β 

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