(a) Consider the initial-value problem dA/dt kA, A(0) = Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8? =

(a) Consider the initial-value problem dA/dt kA, A(0) = Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8? =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 2EA

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