There is a theory that says the rate at which information spreads by word of mouth is proportional to the product of the number of people who have heard the information and the number who have not.Suppose the total population is N.Which of the following differential equations describe the rate, $\frac{d p}{d t}$ , at which the information spreads by word of mouth?
A) $\frac{d p}{d t}=\frac{k p}{(p-N)}$
B) $\frac{d p}{d t}=k p(N+p)$
C) $\frac{d p}{d t}=\frac{k p}{(N-p)}$
D) $\frac{d p}{d t}=k p(N-p)$

Question

Quizplus · Accepted Answer

The correct differential equation is $ \frac{d p}{d t} = k p(N - p) $. This equation models the rate of spread of information as proportional to the product of the number of people who have heard the information ($p$) and the number who have not ($N - p$).

There Is a Theory That Says the Rate at Which dpdt\frac{d p}{d t}dtdp​

There Is a Theory That Says the Rate at Which $\frac{d p}{d t}$