Question 455609
A particular compound decay according to the equation y=ae^(-0.0736t), where t is in days. If the initial amount, a, is 4.8 grams. find the time it would take for half of the compound to decay (the half-life)?
:
the equation for half of the compound decayed
4.8*e(-.0736t) = 2.4 
:
divide both sides by 4.8
e^(-.0736t) = {{{2.4/4.8}}}
e^(-.0736t) = .5
:
find the nat log of both side 
ln(e^(-.0736t)) = ln(.5)
-.0736t*ln(e) = ln(.5)
:
Find the nat log of both sides, (ln(e) = 1)
-.0736t = -.693147
t = {{{(-.693147)/(-.0736)}}}
t = 9.4 days is the half life of the compound
:
:
Check this on a calc:
 enter 4.8*e^(-.0736*9.4) results: 2.4, confirms our solution of t = 9.4 days