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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.

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.

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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 found using the formula:

k = ln(2) / t1/2

Substituting the given half-life into this formula gives:

k = ln(2) / 5730 ≈ 0.000121

So, the exponential decay equation for this problem is:

A = 4 * e^(-0.000121t)

This problem has been solved

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