Most population models are simply a matter of life and death. That is, the growth rate of the number of members of the species depends only on the balance of the birth rate and the death rate. In our first problem we will make the simple assumption that these rates are constant fractions of the current population. For example, consider a population of rabbits. If 25% of the population gives birth to a single offspring in a year, the rate of growth due to births would be 0.25N per year where N is the number of rabbits. Of course, death is important too, and the death rate could depend on another constant. For example if 5% of the rabbits dies per year the death rate would be -0.05N per year. Question: why is the death rate negative?
More generally, we can assume the that birthrate constant is b and the death rate constant is d and therefore the total change in population per year is just