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Stitz-Zeager_College_Algebra_e-book

# A x2 4x y 2 10y 25 b 2x2 36x 2y 2 112 0 c

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Unformatted text preview: t , where N (0) = N0 (read ‘N nought’) is the initial number of organisms and k > 0 is the constant of proportionality which satisﬁes the equation (instantaneous rate of change of N (t) at time t) = k N (t) It is worth taking some time to compare Equations 6.3 and 6.4. In Equation 6.3, we use P to denote the initial investment; in Equation 6.4, we use N0 to denote the initial population. In Equation 6.3, r denotes the annual interest rate, and so it shouldn’t be too surprising that the k in Equation 6.4 corresponds to a growth rate as well. While Equations 6.3 and 6.4 look entirely diﬀerent, they both represent the same mathematical concept. Example 6.5.2. In order to perform arthrosclerosis research, epithelial cells are harvested from discarded umbilical tissue and grown in the laboratory. A technician observes that a culture of twelve thousand cells grows to ﬁve million cells in one week. Assuming that the cells follow The Law of Uninhibited Growth, ﬁnd a formula for the number of cel...
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