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What is the half-life of the isotope?
The decay of 666 mg is given by A(t)=666e^0.017t, where t is time in years. Find the amount left after 92 years, round to the nearest milligram. What is the half-life of the isotope?
I know that the solution to the amount after 92 years is 139 mg. But how do I find how to find the half-life?
1 Answer
- hayharbrLv 77 years ago
For the first just plug in 92 for t on a calculator. And for this to be decay, the exponent should be negative. Is it really -0.017t? if so Mine says 139.39 mg so I agree with you.
Then to get the half life, put in 333 for A(t) since that's half of 666 then solve for t
333 = 666 e ^ (-0.017t)
333/666 = e ^ (-0.017t)
ln (1/2) = ln e^ (-0.017t)
ln (1/2) = -0.017t
so t = ln (1/2) ÷ -0.017; my calc says 40.77 years but check it