So here we have an example problem that says, a population of 200 fish in an isolated pond experiences a per capita birth rate or b of 0.3 and a per capita death rate d of 0.1 in a month. Calculate the population growth rate and the intrinsic rate of increase or r. And so recall from our last lesson video that the intrinsic rate of increase is another way to say the per capita population growth rate. Also, recall that this value of r can be calculated using 2 equations, and those two equations can be seen right here. And in this problem, we're given the values of b and d, which again are the per capita birth and death rates.
So all we need to do is take the difference between the two to get the value of r. And so when we do that, what we get is r=0.3-0.1=0.2, and the units of this are going to be fish per month per fish. So now that we've calculated the value of r as 0.2, we can go ahead and plug that into this equation over here. We also have the value of n0, which is the initial population size given to us as 200 fish. So if we plug those two values in, we can calculate delta n over delta t, which is our population growth rate.
And so we can go ahead and do that now. So what we end up getting is r=deltandeltatdivided byn0, which again is 200 fish. And so if you multiply both sides of the equation by 200, what you'll get is 200×0.2, comes out to 40, and that is going to be equal to the, value of delta n over delta t. And the units of this 40 is going to be fish per month, so forty fish. I'll rewrite it over here.
Forty fish per month. That is going to be what delta n over delta t is. So now that we've calculated delta n over delta t as 40 fish per month, we've calculated the population growth rate, and, of course, we've calculated our 0.2 fish per month per fish, and that is the intrinsic rate of increase. So now that concludes this problem, and I'll see you all on our next video.
