SOLUTION: Please help me answer this word problem:
The rate at which a radioactive isotope disintegrates is proportional to the amount present. If a 30g sample will contain only 20g afte
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The rate at which a radioactive isotope disintegrates is proportional to the amount present. If a 30g sample will contain only 20g afte
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Question 1015192: Please help me answer this word problem:
The rate at which a radioactive isotope disintegrates is proportional to the amount present. If a 30g sample will contain only 20g after ten minutes, what is the half-life of this isotope, correct to the nearest tenth of a minute? Answer this question by first finding the amount y of this isotope as a function of time t(in minutes) in the form y=y0e^kt.
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You can put this solution on YOUR website! The rate at which a radioactive isotope disintegrates is proportional to the amount present. If a 30g sample will contain only 20g after ten minutes, what is the half-life of this isotope, correct to the nearest tenth of a minute? Answer this question by first finding the amount y of this isotope as a function of time t(in minutes) in the form
y = yo*e^(kt)
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20 = 30*e^(k*(1/6))
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e^(k/6) = 2/3
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k/6 = ln(2/3) = -0.4055
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k = -2.4328
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Substitute for "k" in the formula:
y = yo*e^(-2.4328t)
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Note: Half-life means y = yo/2
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Then e^(-2.4328t) = 1/2
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-2.4328t = ln(1/2) = -0.6932
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time = -0.6932/-2.4328 = 0.2849 hrs = 17min 5.7sec
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Cheers,
Stan H.
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