 # 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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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 $=\left(10\text{hours decay factor}{\right)}^{1/10}$
$=\left(0.2785{\right)}^{1/10}$
$=0.8799$
To calculate 5-hour growth/decay factor for the number of mg of caffeine in Diego's body,
5 hours decay factor $=\left(1\text{hours decay factor}{\right)}^{5}$
$=\left(0.8799{\right)}^{5}$
$=0.5274$
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* $\left(0.8799{\right)}^{\left(}1.49\right)$
180=initialAmount* $\left(0.8799{\right)}^{1.49}$.........(1)
Similarly,
The amount of caffeine after 2.49 hours is,
Amount=initial Amount* $\left(0.8799{\right)}^{2.49}$
=initial Amount* $\left(0.8799{\right)}^{1.49+1}$
=initialAmount* $\left(0.8799{\right)}^{1.49}\cdot \left(0.8799\right)$
$=180\cdot \left(0.8799\right)$
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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