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damien's body metabolizes caffeine at a rate of 14.4% per hour (so the amount of caffeine in damien's body decreases by 14.4% each hour). if damien consumes a cup of coffee with 80 mg of caffeine in it, how long will it take for damien's body to metabolize half of the 80 mg of caffeine?

Sagot :

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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