A scientist wants to estimate the age of a piece of wood. The half-life of carbon-14 is 5730 years. Let f(t) represent the percent of carbon-14 that remains in the wood at t years after the wood dies.
I have as the equation f(t)=100(1/2)^t/5730 or f(t)100(.999879)^t. Now, the problem I have is if 20% of the carbon-14 remains, how old is the wood? Do I use f(.20)=100(1/2)^.20/5730? What is the correct way to work this out? Thanks so much for your help!
I have as the equation f(t)=100(1/2)^t/5730 or f(t)100(.999879)^t. Now, the problem I have is if 20% of the carbon-14 remains, how old is the wood? Do I use f(.20)=100(1/2)^.20/5730? What is the correct way to work this out? Thanks so much for your help!
-
f(t) = 20% of 100
f(t) = 20
20 = 100 * (1/2)^(t/5730)
1/5 = (1/2)^(t/5730)
ln(1/5) = (t/5730) * ln(1/2)
-ln(5) = (t/5730) * (-ln(2))
ln(5) / ln(2) = t / 5730
5730 * ln(5) / ln(2) = t
f(t) = 20
20 = 100 * (1/2)^(t/5730)
1/5 = (1/2)^(t/5730)
ln(1/5) = (t/5730) * ln(1/2)
-ln(5) = (t/5730) * (-ln(2))
ln(5) / ln(2) = t / 5730
5730 * ln(5) / ln(2) = t