SOLUTION: The half-life of carbon-11 is 20 minutes. How long will it take for 600g. of carbon-11 to decay to 30g? This problems is solved using logs and A=A(sub 0) e^rt Tried this one

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?
This problems is solved using logs and A=A(sub 0) e^rt
Tried this one three times and do not get the right answer. Help, please, thank you:)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The half-life of carbon-11 is 20 minutes. How long will it take for 600g. of carbon-11 to decay to 30g?
.
A=A(sub 0) e^rt
.
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
.
300 = 600e^(20r)
300/600 = e^(20r)
1/2 = e^(20r)
.5 = e^(20r)
ln(.5) = 20r
ln(.5)/20 = r
.
With the above, we can now answer:
How long will it take for 600g. of carbon-11 to decay to 30g?
.
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

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