SOLUTION: A radioactive material decays according to the law: f(t)=500e^-0.47t where f(0) is the initial amount present in grams and f(t) is the amount present at time t (hours). Determine h
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-> SOLUTION: A radioactive material decays according to the law: f(t)=500e^-0.47t where f(0) is the initial amount present in grams and f(t) is the amount present at time t (hours). Determine h
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Question 64591: A radioactive material decays according to the law: f(t)=500e^-0.47t where f(0) is the initial amount present in grams and f(t) is the amount present at time t (hours). Determine how many hours it will take for the material to decay to 100 grams using either graphic or algebraic methods. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A radioactive material decays according to the law: f(t)=500e^-0.47t where f(0) is the initial amount present in grams and f(t) is the amount present at time t (hours). Determine how many hours it will take for the material to decay to 100 grams using either graphic or algebraic methods
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500*e^-.47t = 100
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Step by step, find t:
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Divide both sides by 500
e^-.47t = 100/500
e^-.47t = .2
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Find the nat log of both sides:
ln(e^-.47t) = ln(.2)
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log equiv of exponents:
-.47t*ln(e) = ln(.2)
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Find the nat log of .2; Remember the natural log of e is 1
-.47t*1 = -1.6093438
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Divide both sides by -.47
t = -1.6093438/-.47
t = +3.424 hrs
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Check on a good calc like a Ti83; key in: 500*(e^(-.47*3.424)) = 100.01 ~ 100
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