Exponential Functions — Question 8

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: $$C(t) = 80e^{-0.35t}$$ where $t$ is the number of hours after the drug is administered.

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

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

• What percentage of the drug is lost every hour?

Round all answers to two decimal places.

Question 8 - Solution

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

(a)

$$C(2)=80e^{-0.7}$$

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

(b)

$$t=\ln(80/10)/0.35$$

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

(c)

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

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