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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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