By presenting them mathematically, we can work out predictions mathematically, then see how well they fit natural populations. These are useful for species where all reproduction occurs at once, and most mortality is seasonal, over short time. These are useful for species that reproduce and die over longer time intervals, and to look at longer term population change where we want to know the overall pattern, not annual fluctuation. Most modeling of population growth is long term, so we ll focus on instantaneous models. Before developing our models, we need to define some standard symbols.
Exponential growth does occur in the short term, however.
When populations are first growing in areas, they will grow according to exponential growth. We can use the model for short term change in populations. To do this, we need to use it in a different form. You will need to use the integrated form of this equation, given at the end of the derivation, to solve problems about exponential growth. It turns out we can figure out what it means if we solve for a specific time, the initial time when we observe our population.