QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
For the following problems, use the exact rates. Write your final answers in a complete sentence with proper grammar and correct spelling.
5. The function $D(h)= 8 e^{- 0.3 h}$ can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug has been administered.
a. How many milligrams will be present after 4 hours?
b. When the number of milligrams reaches 1 , the drug is to be administered again. After how many hours will the drug need to be administered?
6. A radioactive isotope, selenium, used in the creation of medical images of the pancreas, has a half-life of 119.77 days. If 100 milligrams are given to a patient, how many milligrams are left after 20 days?
7. The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists conducted a chemical analysis of samples from the volcano area. The samples contained approximately $62.31 \%$ of its original carbon- 14. How long ago was the last eruption of the volcano? (Use 5730 years for the half-life of carbon- 14.)
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Answer
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Step 1
D(4) = 8e^{-0.3 \times 4} \approx 8e^{-1.2} \approx 3.35 \text{ mg}
So, there will be approximately 3.35 milligrams of the drug in the patient's bloodstream after 4 hours.
Step 2
h = -\frac{\ln\left(\frac{1}{8}\right)}{0.3} \approx 9.16 \text{ hours}
Dividing both sides by 8, we get Taking the natural logarithm of both sides, we obtain So, the drug will need to be administered again after approximately 9.16 hours.
Final Answer
a. After 4 hours, there will be approximately 3.35 milligrams of the drug in the patient's bloodstream. b. The drug will need to be administered again after approximately 9.16 hours. c. After 20 days, there will be approximately 87.54 milligrams of selenium left. d. The last eruption of the volcano was approximately 3270 years ago.
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