Question 212012
How long will it take a sample of radioactive substance to decay half of its
 original amount, if it decays according to the function 
A(t) = 450e^-0.249t , where t is the time in years? 
Round to the nearest hundredth year.
:
Half of original amt: 450/2 = 225 [A(t)]
:
{{{450*e^(-.249t)}}} = 225
divide both sides by 450
{{{e^(-.249t)}}} = {{{225/450}}}
{{{e^(-.249t)}}} = .5
then log equiv of exponents
-.249t*ln(e) = ln(.5)
ln of e is one so we have:
-.249t = -.693
t = {{{(-.693)/(-.249)}}}
t = 2.78 yrs
:
:
Check solution on a calc; enter: 450*e^(-.249*2.78)= 225.2 half the original amt