The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 4 milligrams of 14C.Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.A =
Question
The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 4 milligrams of 14C.Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.A =
Solution
The exponential decay equation is given by the formula:
A = P * e^(-kt)
Where:
- A is the amount of substance left after time t
- P is the initial amount of the substance
- k is the decay constant
- t is the time elapsed
In this case, the initial amount of carbon-14 (P) is 4 milligrams and the half-life (t1/2) is 5730 years.
The decay constant (k) can be calculated using the formula:
k = ln(2) / t1/2
Substituting the given values:
k = ln(2) / 5730 ≈ 0.000121
So, the exponential decay equation for this problem is:
A = 4 * e^(-0.000121t)
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