Solved: A radioactive material, such as the isotope thorium-234, disintegrates at a rate

Chapter 1, Problem 12

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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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