Stitz-Zeager_College_Algebra_e-book

A x 32 y 52 65 b x 32 y 62 20 5 x2

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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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