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1. The logistic function
L
P(t) =
1+e-(t-a)
can be used to model populations which saturate over time. The parameter L determines the carrying
capacity (the maximum population) and a determines the horizontal shift.
(a) Suppose that P(t) models the population of wild deer on Mt. Lemmon t years after 1990. Find the
values of the parameters L and a so that the population 10 years after 1990 is 100 deer and so that the
population is increasing fastest at 5 years. (Assume t = 0) is the year 1990)
(b) What is the carrying capacity for deer in the Mt. Lemmon forest? What was the initial population
of deer (i.e. in 1990)?
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