Question 284179: Could someone please help me with this problem? 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. 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 = 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. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope to the nearest year.
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Note: Since this is a decay function I believe you need a negative
in the exponent.
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Substitute and solve for "t":
(I/2) = I*e^(-0.275t)
(1/2) = e^(-0.275t)
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Take the natural log to get:
-0.275t = ln(1/2)
t = -0.6931../-0.275
t = 2.52 years
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Cheers,
Stan H.
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