Unformatted text preview: ing over 35 years, we ﬁnd that monthly compounding yields A(35) = 2000(1.0059375)12(35)
which is about $24,035.28, whereas continuously compounding gives A(35) = 2000e0.07125(35) which
is about $24,213.18 - a diﬀerence of less than 1%.
Equations 6.2 and 6.3 both use exponential functions to describe the growth of an investment.
Curiously enough, the same principles which govern compound interest are also used to model
short term growth of populations. In Biology, The Law of Uninhibited Growth states as
its premise that the instantaneous rate at which a population increases at any time is directly
proportional to the population at that time.9 In other words, the more organisms there are at a
given moment, the faster they reproduce. Formulating the law as stated results in a diﬀerential
equation, which requires Calculus to solve. Its solution is stated below.
Equation 6.4. Uninhibited Growth: If a population increases according to The Law of Uninhibited Growth, the number of organisms N at time t is given by the formula
N (t) = N0 ek...
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