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Unformatted text preview: graph of y = T (t) is approaching its horizontal
asymptote y = 350 from below. Physically, this means the roast will eventually warm up to 350◦ F.12
The function T is sometimes called a limited growth model, since the function T remains bounded
as t → ∞. If we apply the principles behind Newton’s Law of Cooling to a biological example, it
says the growth rate of a population is directly proportional to how much room the population has
to grow. In other words, the more room for expansion, the faster the growth rate. The logistic
growth model combines The Law of Uninhibited Growth with limited growth and states that the
rate of growth of a population varies jointly with the population itself as well as the room the
population has to grow.
Equation 6.7. Logistic Growth: If a population behaves according to the assumptions of
logistic growth, the number of organisms N at time t is given by the equation
N (t) = L
1 + Ce−kLt where N (0) = N0 is the initial population, L is the limiting populati...
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