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Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics by Robert B. Banks

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23

Growth and Spreading and Mathematical Analogies

How fast does a plant or a person grow? What is the rate of increase of the population of a state or a nation? How quickly does a rumor or a disease spread through a certain community? How rapidly is a new technology adopted in a particular geographical setting? How fast does an innovation replace an established methodology?

To help us obtain answers to these and similar kinds of questions, we need to construct an appropriate mathematical framework. Such a framework is provided by the following simple differential equation:

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in which N is the magnitude of the growing or spreading quantity, t

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