Unformatted text preview: current population reproduces at a ﬁxed rate, so the larger the population the more new organisms are produced. While this is too simple to model most real populations, it is useful in some cases over a limited time. When k < 0, the diﬀerential equation describes a quantity that decreases in proportion to the current value; this can be used to model radioactive decay. The constant solution is y ( t ) = 0; of course this will not be the solution to any interesting initial value problem. For the nonconstant solutions, we proceed much as...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Radioactive Decay

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