xponential growth dN / dt = rate of change of the population. This value should always be increasing faster and faster for true exponential growth, though will slow down eventually to around zero in logistic growth. The equation sheet tells us that dN / dt = B - D (births - deaths, assuming no immigration / emigration occurs), and also that dN / dt = rN That means we can substitute and set those groups equal: B - D = rN and solve for r r = (B - D) / N where N is the total population size So what is r then? It is the per capita rate of increase - or how many offspring each individual might help to reproduce. We can calculate r if we know some basic facts about one generation of a population - then if we assume those trends continue, we can project what might happen to the population size. Here's an example: A population of bacteria currently has 100 total individuals. If the current birth rate is 82 individuals per day and the current death rate is 12 individuals per day, how many individuals would be in the population after 10 days