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. 
:
Ao*2^(-t/h) = A, where
Ao = 200
A = 80
h = 5.7 hrs
t = time of decay
:
200*2^(-t/5.7) = 80
2^(-t/5.7) = {{{80/200}}}
2^(-t/5.7) = .4
using nat logs
{{{-t/5.7}}}ln(2) = ln(.4)
{{{-t/5.7}}}= {{{ln(.4)/ln(2)}}}
using the calc
{{{-t/5.7}}} = -1.32193
t = -5.7 * -1.32193
t = +7.535 ~ 7.5 hrs to decay to 80 mg