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. The half-life of a rodion

Linear Algebra: A Modern Introduction
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Chapter6: Vector Spaces
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Number 12 1.2 differential equations 

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.
The half-life of a rodion
Transcribed Image Text: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. The half-life of a rodion
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