So here we have an example problem that says, a population of 289 wolves has 27 births and 9 deaths from the year 2023 to the year 2024, a period of 1 year. Calculate the per capita birth rate, the per capita death rate, the per capita population growth rate, and the overall population growth rate. And so we're going to perform each of these calculations one-by-one, starting with the per capita birth rate, which is simply the number of births per individual. So, we can take the 27 births that are given to us and divide it by the 289 individual wolves. The calculation gives us an answer of about 0.0934, and the units are going to be births per wolf.

Next, we can calculate the per capita death rate, which is just going to be the number of deaths per individual. We're given that there are 9 deaths, and again, 289 individual wolves. So, \( \frac{9}{289} \) gives us an answer of about 0.0311, and this is going to be in units of deaths per wolf.

So now we can go ahead and calculate the per capita population growth rate, which, recall, is symbolized with the variable \( r \), and can be calculated by taking the difference between the per capita birth rate and the per capita death rate, \( b - d \). And so, \( 0.0934 - 0.0311 \), gives us an answer of 0.0623, and the units of this are going to be wolves per year per wolf. What this means is that each individual wolf contributes 0.0623 wolves to the population per year.

Last but not least, we can calculate the population growth rate, which is simply \( \Delta n \) over \( \Delta t \) or the change in population size over the change in time. We can calculate this in several different ways, but what we're going to do is simply take the difference in the number of births and the number of deaths, which will give us the change of population size, so 27 births minus 9 deaths. Since \( \Delta t \) is just the elapsed time, which is 1 year, so that's going to be 1. Hence, \( 27 - 9 = 18 \), and over 1, it's just going to come out to 18, and the units of this number are going to be wolves per year. And so what we're seeing is that in this time period, there is an overall growth rate of the population going from 289 wolves to 289 plus 18 wolves; 18 additional wolves grew in that year.

And so, this here concludes this example problem, and I'll see you all in our next video.