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Math / Differential Equations 00 4 / Chapter 1.1 / Problem 6

Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall

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Model radioactive decay using the notation t = time

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QUESTION:

Model radioactive decay using the notation t = time (independent variable), r(t) = amount of particular radioactive isotope present at time t (dependent variable), = decay rate (parameter). Note that the minus sign is used so that > 0. (a) Using this notation, write a model for the decay of a particular radioactive isotope. (b) If the amount of the isotope present at t = 0 is r0, state the corresponding initial-value problem for the model in part (a).

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QUESTION:

Model radioactive decay using the notation t = time (independent variable), r(t) = amount of particular radioactive isotope present at time t (dependent variable), = decay rate (parameter). Note that the minus sign is used so that > 0. (a) Using this notation, write a model for the decay of a particular radioactive isotope. (b) If the amount of the isotope present at t = 0 is r0, state the corresponding initial-value problem for the model in part (a).

ANSWER:

Step 1 of 3

(a)

When a specific amount changes at a rate, we let the product of the rate and the amount equal the derivative of the amount.

Rewrite the as the differentiation of and .

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