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4: Exponential Growth and Decay

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This document discusses exponential growth and decay from a calculus perspective, focusing on the mathematical definitions and applications of exponential functions. It covers the differential equations that describe exponential behavior, including population modeling, radioactive decay, Newton's law of cooling, and compounding interest. The section provides examples to illustrate how these concepts are applied in various scientific and practical contexts.

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What is an example of decay?

This equation describes a two phase exponential decay. Y starts out equal to Span1+Span2+PLATEAU and decays to PLATEAU with fast and slow components. The two half-lives are 0.6932/K1 and 0.6932/K2. In the figure, the two rate constants differ tenfold, but the spans were equal.

What is exponential growth and decay?

Some examples include the exponential decrease in the size of a population, amount of a drug remaining in a patients bloodstream, and the decay of certain radioactive isotopes. There are two common models used for exponential decay.

What are 2 examples of exponential decay?

Exponential growth assumes unlimited resources, while logistic growth considers limited resources and carrying capacity. 2. Exponential growth leads to a constantly increasing growth rate, whereas logistic growth starts rapidly and then slows down as the population reaches its carrying capacity.

What is an example of exponential decay?

Exponential equations can have any positive integer as the base number except for one . One raised to any power is just one. Here are two examples that have the same base number: y = 4 x 5 and 4 x + 3 = 2 . The following examples do not have the same base number: 7 = 5 x 10 and 6 3 x = 10 .