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Please help confused with half life /compound interest problems

  1. Fermium-252 decays in 10 minutes to 76.1% of its original

mass. Find the half-life of fermium-252.

  1. How long do you have to wait until 15mg of beryllium-7 have

decayed to 4mg, if the half-life of beryllium-7 is 53.12 days?

Verified Answer :

here2help

Half life means only half of matter is left, which means half is decayed/radiated. 
Formula for half life is
t/2 = [(elapsed time)(log2)]/[log(beginning amount/ending amount)]
1. t/2 = [(10)(log2)]/[log(100/76.1)] = 25.378 minutes.
 t/2 = [10 0.301]/[log 1.314] = [3.01]/[0.1186] = 25.378
2. 53.12 = [(T)(log2)]/[log(15/4)], on solving we get, T = 101.29 days
 53.12 = [T 0.301]/[log 3.75] = [0.301 T]/[0.574],
 T = [53.12 * 0.574]/[0.301] = [30.49]/[0.301] = 101.29

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