Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug. How much will be left after 12 hours?.

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12-04-2022
Mathematics

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Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug. How much will be left after 12 hours?.

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2022-04-22T11:21:06+02:00

The amount of drugs that will be left after 12 hours is 17.42 mg provided Sarah takes 550 mg of an antibiotic every hour.

What is exponential decay?

Exponential decay can be described as a reduced amount of an original substance by a definite percentage over a period of time. It can be determined by using the formula:

[tex]\mathbf{y = a(1 - r)^t}[/tex]

where;

y = total amount,
a = initial amount = 550 mg
r = the growth rate = 0.25
t = number of growth periods = 12 hours

[tex]\mathbf{y = 550(1 - 0.25)^{12}}[/tex]

y = 17.42 mg

Therefore, we can conclude that the amount of drugs that will be left after 12 hours is 17.42 mg.

Learn more about the exponential decay model here:

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