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a. Consider the initial value problem dA/dt = KA. A(0) = A0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -(lin2)/K. b. Show that the solution of the initial value problem in part (a) can be written A(t) = A02-t/T c. If a radioactive substance has the half life T given in part (a) how long will it take an initial amount A0 of the substance to decay to 1/8 A0?

- November 14, 2022 - Edwin Tunner

1a. Consider the initial value problem dA/dt = KA.

A(0) = A0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -(lin2)/K.

b. Show that the solution of the initial value problem in part (a) can be written A(t) = A02-t/T

c. If a radioactive substance has the half life T given in part (a) how long will it take an initial amount A0 of the substance to decay to 1/8 A0?

 

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