SOLUTION: Miguel consumes an energy drink that has 200 mg of caffeine in it and the caffeine leaves his body at a rate of 13.6% per hour. (Assume Miguel has no caffeine in his body when cons

Algebra ->  Finance -> SOLUTION: Miguel consumes an energy drink that has 200 mg of caffeine in it and the caffeine leaves his body at a rate of 13.6% per hour. (Assume Miguel has no caffeine in his body when cons      Log On


   

Question 1123923: Miguel consumes an energy drink that has 200 mg of caffeine in it and the caffeine leaves his body at a rate of 13.6% per hour. (Assume Miguel has no caffeine in his body when consuming the drink.)
a.Write a function f that determines the number of mg of caffeine in Miguel's body in terms of the number of hours t since Miguel consumed the energy drink.
b. How many mg of caffeine is left in Miguel's body 5 hours after he consumed the energy drink?
c. If Miguel has 80 mg of caffeine left in his body, how many hours have elapsed since he consumed the energy drink? (Hint: it might help to use a graphing calculator.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a)
The function is:
+f%28t%29+=+200+-+.136t%2A200+
+f%28t%29+=+200%2A%28+1+-+.136t+%29+
b)
+t+=+5+ hrs
+f%285%29+=+200%2A%28+1+-+.136%2A5+%29+
+f%285%29+=+200%2A%28+1+-+.68+%29+
+f%285%29+=+200%2A.32+
+f%285%29+=+64+
There are 64 mg caffeine left
————————-
c)
+f%28t%29+=+80+
+80+=++200+-+.136%2A200t+
+.136%2A200t+=+200+-+80+
+27.2t+=+120+
+t+=+4.412+ hrs
This is about 4 hrs and 25 min