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Growth of biological populations are often modeled using logistic growth, which posits that some limit will eventually stop a population from increasing in size. The simplest form of this type of growth is logistic growth and takes the following form:

N_tplus1 <- N_t + r * N_t * ((K - N_t) / K)

where N_t is the abundance at time t, N_tplus1 is the abundance at time t+1, r is the maximum per capita reproductive rate, and K is the carrying capacity. The (K - N_t) / K term captures the impact of the members of a species on each other - the more individuals of the species there are, the lower each individuals net reproductive rate.

Working late into the evening your professor has thrown together a small example program that determines the equilibrium population sizes from logistic growth and the time it takes to reach those equilibria. The file is in your repository and is named logistic_growth.R. Unfortunately, he’s gotten sloppy because of the late hour and he’s made a few mistakes. Fix the errors on lines 3 and 13, save the file, and then commit it back to your repository with an appropriate commit message.