The half-life of carbon-14 is 5,730 years. Assuming you start with 100% of carbon-14, what is the expression for the percent, P(t), of carbon-14 that remains in an organism that is t years old and what is the percent of carbon-14 remaining (rounded to the nearest whole percent) in an organism estimated to be 15,000 years old?
Hint: The exponential equation for half-life is P(t) = A0(0.5)t/H, where P(t) is the percent of carbon-14 remaining, A0 is the initial amount (100%), t is age of the organism in years, and H is the half-life.
P(t) = A0(0.5)t/H. This equation is slightly wrong the way you have it written. It should be written like this: P(t) = A0(0.5)^t/H.
There is basically a simpler way to express your equation and it is this:
A=a2^-H, where, a=original amount, A=amount remaining, H=half-life in years.
So, for an organism estimated to be 15,000 years old:
15,000/5,730=2.6178 half-lives, then we have:
A=a2^-2.6178
A=1. 0.1629 X 100
A=16.29% Left in the organism after 15,000 years.
