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# Which equation determines the percent of an initial amount of the isotope remaining after t years?

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Which equation determines the percent of an initial amount of the isotope remaining after t years?

SamJones  Mar 1, 2018
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amount after  0  years  =  N

amount after  5.27 years  =  (1/2)N

amount after  2 * 5.27 years  =  (1/2)(1/2)N

amount after  3 * 5.27 years  =  (1/2)(1/2)(1/2)N  =  (1/2)3N

amount after  x * 5.27 years  =  (1/2)xN

x * 5.27  =  t

x  =  t / 5.27

amount after  t  years  =  (1/2)t / 5.27N

amount after  t  years  =  $$(\frac12)^{\frac{t}{5.27}}N$$

$$A=(\frac12)^{\frac{t}{5.27}}N\\ A=N(\frac12)^{\frac{t}{5.27}}$$

If the initial amount is  100, then...

$$A=100(\frac12)^{\frac{t}{5.27}}$$

hectictar  Mar 4, 2018

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