A typical horizontal parabola is sketched below d v 4

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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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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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