<PRE><B>Question 1178995</B>
20 grams of an unknown compound decays continuously according to the model:
 A = 20e-0.02t where A is the amount of the compound remaining after t years.
 How long before the amount of compound reaches one-fourth of its original amount?
:
1/4 of 20 grams is 5 grams, therefore
{{{20*e^(-.02t) = 5}}}
:
{{{e^(-.02t) = 5/20}}}
:
{{{e^(-.02t) = .25}}}
using natural logs
-.02t*ln(e) = ln(2.5)
ln of e is 1, therefore
-.02t = -1.3863
t = -1.3863/-.2
t = 69.3 years
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