Q114. A totalitarian country that prohibits migration has a birth rate b and a death rate d. How does the population change from one year to the next?

We can interpret "birth rate" or "death rate" in two ways — as a rate, for example, deaths per 100 people — or as an absolute number, for example, 5 people per year. In general, we will mean the former.

Let $P_{i}$ be the population in year i. Write an expression for the population in year i+1. If the population in a given year is 100 and birth rate, b, is 5% and the death rate, d, is 6%, write out the population for the next 5 years.