Diego consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Diego's body decreases exponentiall

ruigE 2021-02-25 Answered
Diego consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Diegos
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Expert Answer

i1ziZ
Answered 2021-02-26 Author has 92 answers

Given that:
Diego consumes an energy drink that contains caffeine. The amount of caffeine in Diego's body decreases exponentially.
10-hour decay factor for the number of mg of caffeine in Diego's body is 0.2785
1.
To calculate 1 hours decay factor,
1 hours decay factor =(10hours decay factor)1/10
=(0.2785)1/10
=0.8799
To calculate 5-hour growth/decay factor for the number of mg of caffeine in Diego's body,
5 hours decay factor =(1hours decay factor)5
=(0.8799)5
=0.5274
Hence 5-hour growth/decay factor for the number of mg of caffeine in Diego's body is 0.5274
To calculate 1-hour growth/decay factor for the number of mg of caffeine in Diego's body,
1 hours decay factor =0.8799 (as calculated above)
Hence 1-hour growth/decay factor for the number of mg of caffeine in Diego's body is 0.8799
3.
Given that:
If there were 180 mg of caffeine in Diego's body 1.49 hours after consuming the energy drink.
The amount of caffeine after 1.49 hours is,
Amount=initialAmount* (0.8799)(1.49)
180=initialAmount* (0.8799)1.49.........(1)
Similarly,
The amount of caffeine after 2.49 hours is,
Amount=initial Amount* (0.8799)2.49
=initial Amount* (0.8799)1.49+1
=initialAmount* (0.8799)1.49(0.8799)
=180(0.8799)
from equation(1)
=158.382
Hence 158.382 mg of caffeine is in Diego's body 2.49 hours after consuming the energy drink.

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