7. 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 milligrams (mg) of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate T. (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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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7. 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 milligrams (mg) of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate
T.
(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.
Transcribed Image Text:7. 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 milligrams (mg) of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate T. (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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