SOLUTION: 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 compo

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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)?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F4.8
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 = %28-.693147%29%2F%28-.0736%29
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