According to the logistic growth equation
dNdt=rN(K−N)K
a. the nu...

Question

According to the logistic growth equation
dNdt=rN(K−N)K
a. the number of individuals added per unit time is greatest when N is close to zero.
b. the per capita population growth rate increases as N approaches K.
c. population growth is zero when N equals K.
d. the population grows exponentially when K is small.

Accepted Answer

Hello everyone. And in today's video we have the following problem. The population growth rates is zero in the logistics growth model. When we're given a few just scenarios of the values of the variables in this logistic growth model that we need to just look over and identify which one will yield zero in terms of the population growth rate. So let's visualize this logistic growth model and see what each of the variables in it mean. We have that the narrative of N which is the population at time T is equal to these are value which is a constant. So we don't need to really worry about it. Times end, which again is the population at times T. Which is multiplying this fraction that we see here which is K. In terms of the carrying capacity minus and divided by N. So all of the scenarios relate the values of N. And K. And so the or the position where they're being related in our answer choice is going to be here in terms of the numerator of a fraction. And so if we want to make the population growth rate or just these right side of the equation equals zero. The way that we do this is by making these two values equal to each other. And the reason for this is that if we make them equal to each other, this numerator is going to be zero and the division of zero by any number is going to yield a value of zero. Once we multiply zero by this part of the equation again that is going to be equal to zero. So we're going to have that the derivative of N. Or the population growth rate is going to be zero, which is exactly what we're being asked for. So looking at our answer choices, that is going to be answer choice C. So making the population and the current capacity equal is going to yield the growth rate of zero as we see here. And if we think about it, in terms of just a community standpoint, the carrying capacity is the maximum amount of members that the community can accept. So if the community has a population that is maximum of what it can accept, it won't grow anymore because it's a maximum carrying capacity. And so the population growth will be zero, which is what we see here in the end of our answer choice. So it makes sense. And so that is going to be your final answer and the end of our video. I really hope it helped you and I hope to see you on the next one.

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