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Calculus IChapter 1: ReviewSection 1-7

Exponential Functions — Question 8

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Question 8

A certain medication is administered intravenously and metabolized by the body over time. The amount of the drug in the bloodstream (in milligrams) is modeled by the function: C(t)=80e−0.35tC(t) = 80e^{-0.35t} where tt is the number of hours after the drug is administered.

  • (a) What is the amount of the drug in the bloodstream after 2 hours?

  • (b) After how many hours will only 10 mg remain in the bloodstream?

  • (c) What percentage of the drug is lost every hour?

Round all answers to two decimal places.

Original worksheet page 1: question and worked solution for 1-7-008
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Question 8 - Solution

Use the exact exponential model and keep full precision until the final rounding.

(a)

C(2)=80e−0.7C(2)=80e^{-0.7}

39.73mg\boxed{39.73\quad\text{mg}}

(b)

t=ln⁡(80/10)/0.35t=\ln(80/10)/0.35

5.94hours\boxed{5.94\quad\text{hours}}

(c)

100(1−C(t+1)/C(t))=100(1−e−0.35)100(1-C(t+1)/C(t))=100(1-e^{-0.35})

29.53%\boxed{29.53\quad\text{\%}}

Original worksheet page 2: question and worked solution for 1-7-008

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