Question

A can of Mountain Dew has 56 mg of caffeine. How long would it take to have less than 12 milligrams of caffeine in your body after finishing this drink?

Answer 1

given
at t = 0, Mo = 56 mg
at time t, M = 12 mg

t = ?

we know, half life of caffeine, T1/2 = 5 hours

decay constant of caffeine, lamda = 0.693/(T1/2)

= 0.693/5

= 0.1386 hour^-1

after time t,

remaining caffeine,

M = Mo*e^(-lamda*t)

M/Mo = e^(-lamda*t)

ln(M/Mo) = -lamda*t

==> t = -ln(M/Mo)/lamda

= -ln(12/56)/0.1386

= 11.1 hours <<<<<<<<<<<<<<<------------------Answer

Note : If the half life of caffeine is not 5 hours in youyr text book. please substitute the given half time in the above equation. you will get the correct answer. just substutute your value in the place of 5 hours.