Take the natural log of both sides of this equation to get ln(.2) = ln(e ^ (-.000120968094 * t)). The same equation is used, only this time you know the value of r but don't know the value of t. You now know the value of r and you want to know how long it will take to have 20% of the original carbon 14 still in the bones. Solve for r to get r = -1.20968094 * 10 ^ -4).Ĭonfirm by replacing r in the original equation with that to get. Since ln(e ^ (r * 5730) = r * 5730 * ln(e), and since ln(e) = 1, then your equation becomes:ĭivide both sides of this equation by 5730 to get ln(.5) / 5730 = r Take the natural log of both sides of this equation to get ln(.5) = ln(e ^ (r * 5730)). If the half life of carbon 14 is 5730 years, then your formula becomes: If you assume the present value is 1, then the half life will be. The time period in this problem is in years.

If the growth rate is negative, then you are dealing with decay.

If the growth rate is positive, then you are dealing with growth. This is the formula that's most often used for determining growth rate of natural events. The formula for continuous compounding is f = p * e ^ (r * t).

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Half life of carbon 14 formula