document.write( "Question 1005366: The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains 200 mg of caffeine. How long after drinking a shot of 5-hour Energy will it take for the amount of caffeine in a person's system to decay to 80mg? Label your answer and round it to one decimal place. Recall: A=A02^-t/h \n" ); document.write( "

Algebra.Com's Answer #621667 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains 200 mg of caffeine.
\n" ); document.write( " How long after drinking a shot of 5-hour Energy will it take for the amount of caffeine in a person's system to decay to 80mg?
\n" ); document.write( " Label your answer and round it to one decimal place.
\n" ); document.write( ":
\n" ); document.write( "Ao*2^(-t/h) = A, where
\n" ); document.write( "Ao = 200
\n" ); document.write( "A = 80
\n" ); document.write( "h = 5.7 hrs
\n" ); document.write( "t = time of decay
\n" ); document.write( ":
\n" ); document.write( "200*2^(-t/5.7) = 80
\n" ); document.write( "2^(-t/5.7) = $\"80%2F200\"$
\n" ); document.write( "2^(-t/5.7) = .4
\n" ); document.write( "using nat logs
\n" ); document.write( " $\"-t%2F5.7\"$ ln(2) = ln(.4)
\n" ); document.write( " $\"-t%2F5.7\"$ = $\"ln%28.4%29%2Fln%282%29\"$
\n" ); document.write( "using the calc
\n" ); document.write( " $\"-t%2F5.7\"$ = -1.32193
\n" ); document.write( "t = -5.7 * -1.32193
\n" ); document.write( "t = +7.535 ~ 7.5 hrs to decay to 80 mg
\n" ); document.write( " \n" ); document.write( "

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