SOLUTION: The half-life of tritium is 12.4 years. How long will it take for 20% of a sample of tritium to decompose? Please round the answer to the nearest tenth. -log5= -t/12.4 log2 --

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The half-life of tritium is 12.4 years. How long will it take for 20% of a sample of tritium to decompose? Please round the answer to the nearest tenth. -log5= -t/12.4 log2 --      Log On


   

Question 613570: The half-life of tritium is 12.4 years. How long will it take for 20% of a sample of tritium to decompose?
Please round the answer to the nearest tenth.
-log5= -t/12.4 log2 --> 12.4(log5\log2)=t --> t=28.8
I know this is incorrect
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
N = P*e^(-kt)

1/2P = P*e^(-k*12.4)

1/2 = e^(-12.4k)

ln(1/2) = -12.4k

-0.693147 = -12.4k

-0.693147/(-12.4) = k

0.05589895 = k

k = 0.05589895
--------------------------------------

N = P*e^(-kt)

N = P*e^(-0.05589895t)

0.8P = P*e^(-0.05589895t)

0.8 = e^(-0.05589895t)

ln(0.8) = -0.05589895t

-0.22314355 = -0.05589895t

-0.22314355/(-0.05589895) = t

3.9919095 = t

t = 3.9919095

So it will take roughly 3.9919095 years for 20% of the sample to decompose.