Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacityM of the environment. That is, if the whale population is aboveM, then it will experience a decline because the environment cannot sustain that large a population level. In the following model, an represents the whale population after n years. Build a numerical solution for M = 5000, m = 100, k = 0.0001, and a₀ = 4000.

Now experiment with different values for M, m, and k. Try several starting values for a₀. What does your model predict?

Transcribed Image Text:

an+1-an k(M-an) (an-m)