SOLUTION: Ethan consumes an energy drink that has 240 mg of caffeine in it and the caffeine leaves his body at a rate of 13.2% per hour. (Assume Ethan has no caffeine in his body when consum

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Question 1128843: Ethan consumes an energy drink that has 240 mg of caffeine in it and the caffeine leaves his body at a rate of 13.2% per hour. (Assume Ethan has no caffeine in his body when consuming the drink.)
A)Write a function f that determines the number of mg of caffeine in Ethan's body in terms of the number of hours t since Ethan consumed the energy drink.
B)How many mg of caffeine is left in Ethan's body 7 hours after he consumed the energy drink?
C)If Ethan has 40 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 josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
y=240%2A%281-0.132%29%5Ex

highlight%28y=240%2A0.868%5Ex%29


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C)If Ethan has 40 mg of caffeine left in his body, how many hours have elapsed
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240%2A0.868%5Ex=40
0.868%5Ex=4%2F24
0.868%5Ex=1%2F6
log%28%280.868%5Ex%29%29=log%28%281%2F6%29%29
x=%281%2Flog%28%280.868%29%29%29%2Alog%28%281%2F6%29%29
about 12.6 hours