12) Two drugs are administered to a patient at the same time every day, and unfortunately they have an adverse reaction to one another. Suppose the concentration of the first drug is D₁ (measured in mg/ml.) after the injection on the nth day (with Do = 0). If it were taken alone, before the injection the next day 80% of the drug present on the preceding day would remain in the blood stream, and the standard daily dose would raise the concentration by 4 mg/ml. Suppose the concentration of the second drug is B₁ (measured in mg/mL) after the injection on the nth day (with Bo = 0). If it were taken alone, before the injection the next day 70% of the drug present on the preceding day would remain in the blood stream, and the standard daily dose would raise the concentration by 5 mg/mL. These two drugs interact in a way which causes a portion of each drug to be filtered out in the kidneys and passed through urine. The additional amount of each drug which is filtered out on a given day is equal to 30% of the amount of the second drug present in the system the previous day. What will the concentration of each drug be on Day 5? What will the concentrations approach over a long period of time? D5- B5- lim Dn. 7248 lim Bn- 72400
12) Two drugs are administered to a patient at the same time every day, and unfortunately they have an adverse reaction to one another. Suppose the concentration of the first drug is D₁ (measured in mg/ml.) after the injection on the nth day (with Do = 0). If it were taken alone, before the injection the next day 80% of the drug present on the preceding day would remain in the blood stream, and the standard daily dose would raise the concentration by 4 mg/ml. Suppose the concentration of the second drug is B₁ (measured in mg/mL) after the injection on the nth day (with Bo = 0). If it were taken alone, before the injection the next day 70% of the drug present on the preceding day would remain in the blood stream, and the standard daily dose would raise the concentration by 5 mg/mL. These two drugs interact in a way which causes a portion of each drug to be filtered out in the kidneys and passed through urine. The additional amount of each drug which is filtered out on a given day is equal to 30% of the amount of the second drug present in the system the previous day. What will the concentration of each drug be on Day 5? What will the concentrations approach over a long period of time? D5- B5- lim Dn. 7248 lim Bn- 72400
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:12) Two drugs are administered to a patient at the same time every day, and unfortunately they have
an adverse reaction to one another.
Suppose the concentration of the first drug is D₁ (measured in mg/mL) after the injection on the
nth day (with Do = 0). If it were taken alone, before the injection the next day 80% of the drug
present on the preceding day would remain in the blood stream, and the standard daily dose
would raise the concentration by 4 mg/mL.
Suppose the concentration of the second drug is B₁ (measured in mg/mL) after the injection on
the nth day (with Bo= 0). If it were taken alone, before the injection the next day 70% of the
drug present on the preceding day would remain in the blood stream, and the standard daily dose
would raise the concentration by 5 mg/mL.
These two drugs interact in a way which causes a portion of each drug to be filtered out in the
kidneys and passed through urine. The additional amount of each drug which is filtered out on a
given day is equal to 30% of the amount of the second drug present in the system the previous
day.
What will the concentration of each drug be on Day 5? What will the concentrations approach
over a long period of time?
D5.
B5.
lim Dn-
72-00
lim Bn.
71-00
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