A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t, then dQ/dt = −rQ, where r > 0 is the decay rate. a.If 100 mg of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate r. b.Find an expression for the amount of thorium-234 present at any time t. c.Find the time required for the thorium-234 to decay to one-half its original amount.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
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A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t, then dQ/dt = −rQ, where r > 0 is the decay rate.

a.If 100 mg of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate r.

b.Find an expression for the amount of thorium-234 present at any time t.

c.Find the time required for the thorium-234 to decay to one-half its original amount.

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