Unformatted text preview: ned from its purchase price of $25,000 to nothing at all. Another real
world phenomenon which follows suit is radioactive decay. There are elements which are unstable
and emit energy spontaneously. In doing so, the amount of the element itself diminishes. The
assumption behind this model is that the rate of decay of an element at a particular time is directly
proportional to the amount of the element present at that time. In other words, the more of the
element there is, the faster the element decays. This is precisely the same kind of hypothesis which
drives The Law of Uninhibited Growth, and as such, the equation governing radioactive decay is
hauntingly similar to Equation 6.4 with the exception that the rate constant k is negative.
Equation 6.5. Radioactive Decay The amount of a radioactive element A at time t is given
by the formula
A(t) = A0 ekt ,
where A(0) = A0 is the initial amount of the element and k < 0 is the constant of proportionality
which satisﬁes the equation
(instantaneous rate of change of A(t) at time t) = k A(t)
Example 6...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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