Question

you buy a monster energy drink that gas 86mg of caffeine In it. each hour the amount of caffeine in your body decreases by 12%. how much caffeine will be left in your system 3 hours later?

Answer 1

Step 1: Write out the formula for computing the amount of caffeine left

After 1 hour,

C = (1-0.12)86=0.88x86mg

After 2 hour,

C = (1-0.12)0.88x86=0.88²x86mg

Therefore,

After n hours,

$C=0.88^n\times86mg$

Where,

$\begin{gathered} C=\text{ the amount of caffeine left} \\ n=\text{ the number of hours after taking the monster energy drink} \end{gathered}$

Step 2: Write out the given value and substitute it into the formula to find the amount of caffeine left

$n=3\text{ hours}$

Therefore,

$C=0.88^3\times86=58.6mg$

Hence after 3 hours, the amount of caffeine left in your system is 58.6mg