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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