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

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.