Answer :
By using the concept of Depreciation, it is obtained that
Damien's body  metabolize half of the 80 mg of caffeine in 4.5 hours
What is Depreciation?
Depreciation is the reduction in the value of a product at a certain rate over a certain period of time.
Here the concept of Depreciation has been used
Let the time taken to metabolize half of the 80 mg of caffeine be t hours
Damien's body metabolizes caffeine at a rate of 14.4% per hour
By the problem,
[tex]80(1 - \frac{14.4}{100})^t = 40\\\\(\frac{100 - 14.4}{100})^t = \frac{40}{80}\\\\(\frac{85.6}{100})^t = \frac{1}{2}\\\\(\frac{107}{125})^t = \frac{1}{2}\\\\[/tex]
[tex]t (ln (\frac{107}{125})) = -0.693\\\\[/tex]
-0.155 t = - 0.693
t = [tex]\frac{-0.693}{-0.155}\\[/tex]
t = 4.5 hour
To learn more about Depreciation, refer to the link-
https://brainly.com/question/25806993
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