Question 301593: 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. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life
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N(t) = Ie^(kt)
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(1/2)I = I*e^(-0.275t)
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e^(-0.275t) = 0.5
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Take the natural log and solve for "t":
-0.275t = ln(0.5)
t = 2.52 years (half-life)
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Cheers,
Stan H.
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