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1. A drug's effectiveness decreases over time. If each hour, a drug is only 90% as effective as during the previous hour, at some point the patient will not be receiving enough medication and will need another dose. This can be modeled by the exponential function y= y.(0.90)-l. In this equation y, is the amount of the initial dose, and y is the amount of the medication still available "t" hours after the drug was administered. Suppose the initial dose was 200 mg. How long will it take for this initial dose to reach the dangerously low level of 50 mg? Solve this problem algebraically, not with a graph or by plugging and checking.

1. A drug's effectiveness decreases over time. If each hour, a drug is only 90% as effective as during the previous hour, at some point the patient will not be receiving enough medication and will need another dose. This can be modeled by the exponential function y= y.(0.90)-l. In this equation y, is the amount of the initial dose, and y is the amount of the medication still available "t" hours after the drug was administered. Suppose the initial dose was 200 mg. How long will it take for this initial dose to reach the dangerously low level of 50 mg? Solve this problem algebraically, not with a graph or by plugging and checking.

Advanced Engineering Mathematics
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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1. A drug's effectiveness decreases over time. If each hour, a drug is only 90% as effective as during the previous hour, at some point the patient will not be receiving enough medication and will need another dose. This can be modeled by the exponential function \( y = y_0 (0.90)^t \). In this equation, \( y_0 \) is the amount of the initial dose, and \( y \) is the amount of the medication still available "t" hours after the drug was administered. Suppose the initial dose was 200 mg. How long will it take for this initial dose to reach the dangerously low level of 50 mg? Solve this problem algebraically, not with a graph or by plugging and checking.
Transcribed Image Text:1. A drug's effectiveness decreases over time. If each hour, a drug is only 90% as effective as during the previous hour, at some point the patient will not be receiving enough medication and will need another dose. This can be modeled by the exponential function \( y = y_0 (0.90)^t \). In this equation, \( y_0 \) is the amount of the initial dose, and \( y \) is the amount of the medication still available "t" hours after the drug was administered. Suppose the initial dose was 200 mg. How long will it take for this initial dose to reach the dangerously low level of 50 mg? Solve this problem algebraically, not with a graph or by plugging and checking.
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