SOLUTION: A 1200 kg of a radioactive element kept decaying for 50 years until 300 kg of the element remained. What is the half-life of the element? I can not figure this answer out! Please h

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Question 814289: A 1200 kg of a radioactive element kept decaying for 50 years until 300 kg of the element remained. What is the half-life of the element? I can not figure this answer out! Please help
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A 1200 kg of a radioactive element kept decaying for 50 years until 300 kg of the element remained.
What is the half-life of the element?
:
The radioactive decay formula: A = Ao*2^(-t/h), WHERE:
A = Amt remaining after t time (300 mg)
Ao = initial amt (t=0) (1200 mg)
t = time of decay (50 yrs)
h = half-life of substance
:
1200*2^(50/h) = 300
2^(-50/h) = 300%2F1200
2^(-50/h) = .25
log[2^(-50/h)] = log(.25)
log equiv of exponents
-50%2Fhlog(2) = log(.25)
-50%2Fh = log%28.25%29%2Flog%282%29
using your calc
-50%2Fh = -2
h = %28-50%29%2F%28-2%29
h = +25 yrs is the half life
:
:
Check this on your calc, enter 1200*2^(-50/25) results: 300