suppose a population always grows at a rate equal to 1/300 of the population size (measured in members per…

suppose a population always grows at a rate equal to 1/300 of the population size (measured in members per year). write a differential equation that represents this relationship. (let ( p(t) ) represent the population ( t ) years from now.) ( \frac{dp}{dt}= )

suppose a population always grows at a rate equal to 1/300 of the population size (measured in members per year). write a differential equation that represents this relationship. (let ( p(t) ) represent the population ( t ) years from now.) ( \frac{dp}{dt}= )

Answer

Explanation:

Step1: Recall the general form of a differential equation for population growth

The general form of a differential equation for population growth is (\frac{dp}{dt}=kp), where (k) is the growth - rate constant and (p = p(t)) is the population at time (t).

Step2: Identify the value of (k)

We are given that the growth rate is equal to (\frac{1}{300}) of the population size. So, when we compare with (\frac{dp}{dt}=kp), we can see that (k=\frac{1}{300}).

Answer:

(\frac{dp}{dt}=\frac{1}{300}p)