Question 220596
The half-life of carbon-11 is 20 minutes.  How long will it take for 600g. of carbon-11 to decay to 30g?
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A=A(sub 0) e^rt
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Since the "half-life" is 20 minutes, we will have "half" the material so:
A = 300
A(sub0) = 600 (amount we started with)
t = 20 
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300 = 600e^(20r)
300/600 = e^(20r)
1/2 = e^(20r)
.5 = e^(20r)
ln(.5) = 20r
ln(.5)/20 = r
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With the above, we can now answer:
How long will it take for 600g. of carbon-11 to decay to 30g?
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30 = 600e^(t(ln(.5)/20))
30/600 = e^(t(ln(.5)/20))
1/20 = e^(t(ln(.5)/20))
ln(1/20) = t(ln(.5)/20)
ln(1/20)/[ln(.5)/20] = t
86.44 minutes = t

ln(1/20)/ln(.5) = t