SOLUTION: 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 y
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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 hundreth year.
choices (in years):
2.78
112.05
24.54
27.32 Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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)]
: = 225
divide both sides by 450 = = .5
then log equiv of exponents
-.249t*ln(e) = ln(.5)
ln of e is one so we have:
-.249t = -.693
t =
t = 2.78 yrs
:
:
Check solution on a calc; enter: 450*e^(-.249*2.78)= 225.2 half the original amt
