Drug Concentration A drug is administered to a patient, and the concentration of the drug in the bloodstream is monitored. At time t ≥ 0 (in hours since giving the drug) the concentration (in mg/L) is given by
Graph the function c with a graphing device.
- (a) What is the highest concentration of drug that is reached in the patient’s bloodstream?
- (b) What happens to the drug concentration after a long period of time?
- (c) How long does it take for the concentration to drop below 0.3 mg/L?
(a)
The highest concentration of drug that is reached in the patient’s bloodstream.
Answer to Problem 85E
The highest concentration of drug reached in the patient’s bloodstream is 2.5 mg/L.
Explanation of Solution
Given:
The drug concentration in the bloodstream is given below,
Where tis the time in hours since giving the drug c is the concentration of drug in bloodstream in mg/L.
Calculation:
The given rational function is
Sketch the graph of given rational function by graphing device,
Figure (1)
The highest concentration of drug is the maximum point in graph of rational function.
From the graph, the local maximum is
(b)
The drug concentration after a long period of time.
Explanation of Solution
From the Figure (1), it can be noticed that the graph of rational function decreases at the time increases.
Thus, the concentration of drug decreases to 0 after a long period of time.
(c)
The time for the concentration to drop below 0.3 mg/L.
Answer to Problem 85E
The time for the concentration to drop below 0.3 mg/L is 16.6 hours.
Explanation of Solution
Given:
The drug concentration in the bloodstream is given below,
Where t is the time in hours since giving the drug and c is the concentration of drug in bloodstream in mg/L.
Calculation:
Substitute 0.3 for
Solve the above quadratic equation by following formula which is used to find the solutions for x if the quadratic equation is
Substitute t for x, 5 for b, 0.3 for c and 0.3 for a in above given formula,
Take positive sign first and find the value of t,
Take negative sign and find the value of t,
From the Figure (1), the value of t, where the concentration drops below 0.3 mg/L is 16.6.
Thus, the time for the concentration to drop below 0.3 mg/L is 16.6 hours.
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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