Question 285443: Use the formula N = Iekt, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. An artifact is discovered at a certain site. If it has 65% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the formula N = Ie^(kt), where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time.
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An artifact is discovered at a certain site. If it has 65% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.)
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Note: Since this is a decay function, k is negative in the exponent.
0.65I = I*e^(-0.0125t)
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e^(-0.0125t) = 0.65
Take the natural log of both sides and solve for "t":
-0.0125t = ln(0.65)
t = 34.46 years (time for the initial amount to decay 35%.
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Cheers,
Stan H.
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