document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #46511 by ankor@dixie-net.com(22740)\"\" \"About 
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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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\n" ); document.write( "500*e^-.47t = 100
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\n" ); document.write( "Step by step, find t:
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\n" ); document.write( "Divide both sides by 500
\n" ); document.write( "e^-.47t = 100/500
\n" ); document.write( "e^-.47t = .2
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\n" ); document.write( "Find the nat log of both sides:
\n" ); document.write( "ln(e^-.47t) = ln(.2)
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\n" ); document.write( "log equiv of exponents:
\n" ); document.write( "-.47t*ln(e) = ln(.2)
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\n" ); document.write( "Find the nat log of .2; Remember the natural log of e is 1
\n" ); document.write( "-.47t*1 = -1.6093438
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\n" ); document.write( "Divide both sides by -.47
\n" ); document.write( "t = -1.6093438/-.47
\n" ); document.write( "t = +3.424 hrs
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\n" ); document.write( "Check on a good calc like a Ti83; key in: 500*(e^(-.47*3.424)) = 100.01 ~ 100
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\n" ); document.write( "did this help?\r
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