SOLUTION: Radioactive carbon-14 decays according to the function Q(t)=Qoe^-0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Qo is the amount of present at ti

Question 277451: Radioactive carbon-14 decays according to the function Q(t)=Qoe^-0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Qo is the amount of present at time t=0. Estimate the age of a skull if 23% of the original quantity of carbon-14 remains.
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Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Radioactive carbon-14 decays according to the function Q(t)=Qoe^-0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Qo is the amount of present at time t=0. Estimate the age of a skull if 23% of the original quantity of carbon-14 remains.
.
Q(t)=Qoe^-0.000121t
.
Plugging in:
.23(Qo) = (Qo)e^-0.000121t
Now, we solve for t
first, divide both sides by Qo:
.23 = e^-0.000121t
take the natural log of both sides:
ln(.23) = -0.000121t
ln(.23)/(-0.000121) = t
12,146 years = t

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