# math with application

posted by liv

If 12 % of a radioactive substance decays in 7 hours, what is the half-life of the substance?

Carry out all calculations exactly, then round the final answer to three decimal places.

The half life is what hours?

1. bobpursley

an interesting thought, carrying out log calculations exactly. Would require an infinite amount time adding up an infinite series.

But more practical, not exact, but using approximations from ones calculator.. if .12 decays,then .88 remains..

.88=e^(t*ln(.5)/th)
t=7hrs, solve for th

take ln of each side
ln (.88)=-ln(.5)*7 / th
thalflife= 7(ln(.5)/ln.88

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