A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient's bloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient's blood, but there needs to be at least 2 mg in the patient's blood for it to be effective. (a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in the patient's blood immediately after taking the nth dose, and think about what must be true about An to ensure a safe dosing schedule. Write out very carefully what A1, A2, A3 are before trying to find a pattern for An.) (b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in the patient's blood immediately before taking the nth dose.)
A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient's bloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient's blood, but there needs to be at least 2 mg in the patient's blood for it to be effective. (a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in the patient's blood immediately after taking the nth dose, and think about what must be true about An to ensure a safe dosing schedule. Write out very carefully what A1, A2, A3 are before trying to find a pattern for An.) (b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in the patient's blood immediately before taking the nth dose.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 2 A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient's
bloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient's
blood, but there needs to be at least 2 mg in the patient's blood for it to be effective.
(a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in the
patient's blood immediately after taking the nth dose, and think about what must be true about
An to ensure a safe dosing schedule. Write out very carefully what A1, A2, A3 are before trying
to find a pattern for An.)
(b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in the
patient's blood immediately before taking the nth dose.)
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