SOLUTION: Brayden's body metabolizes caffeine at a rate of 13.7% per hour (so the amount of caffeine in Brayden's body decreases by 13.7% each hour). If Brayden consumes a cup of coffee w

Algebra ->  Finance -> SOLUTION: Brayden's body metabolizes caffeine at a rate of 13.7% per hour (so the amount of caffeine in Brayden's body decreases by 13.7% each hour). If Brayden consumes a cup of coffee w      Log On


   

Question 1149031: Brayden's body metabolizes caffeine at a rate of 13.7% per hour (so the amount of caffeine in Brayden's body decreases by 13.7% each hour).
If Brayden consumes a cup of coffee with 96 mg of caffeine in it, how long will it take for Brayden's body to metabolize half of the 96 mg of caffeine?
hours
If Brayden consumes an energy drink with 184 mg of caffeine in it, how long will it take for Brayden's body to metabolize half of the 184 mg of caffeine?
hours
If Brayden consumes a cup of coffee with c mg of caffeine in it, how long will it take for Brayden's body to metabolize half of the
c mg of caffeine? (Hint: your answer will be a numerical value.)
hours
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If each hour, 13.7% is metabolized, then unmetabolized is 1-0.137=0.863, fraction.

y=c%2A0.863%5Ex
y, amount present milligrams caffeine
x, time passed in hours
c, initial amount

If y=c/2 then 1%2F2=1%2A0.863%5Ex
Solve for x.
(Half-Life)