3. A drug is administered to a patient, and the concentration of the drug in the bloodstream is monitored. At time t 20 (in hours since giving the drug), the concentration (in mg/L) is given by 5t c(t) : t2 + 1 Graphing this may still help you here. a. What is the highest concentration of drug that is reached in the patient's bloodstream? When would this approximately happen? b. How long does it take for the concentration to drop below 0.3 mg/L? Give the domain and range of this function, in context, using interval notation. d. Many rational functions have vertical asymptotes as a feature of their graphs. Why does c(t) have no vertical asymptotes? EXPLAIN HOW THIS FUNCTION COULD HAVE ASYMPTOTES, C. IGNORE CONTEXT IF NECESSARY. e. Find lim c(t). Explain your answer in the context of the problem. t→0∞

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter5: Polynomial And Rational Functions
Section5.6: Rational Functions
Problem 81SE: For the following exercises, express a rational function that describes the situation. 81. A large...
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Rational Functions:
3. 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
5t
c(t)
t2 + 1
Graphing this
still help you here.
may
a. What is the highest concentration of drug that is reached in the patient's bloodstream?
When would this approximately happen?
b. How long does it take for the concentration to drop below 0.3 mg/L?
c. Give the domain and range of this function, in context, using interval notation.
d. Many rational functions have vertical asymptotes as a feature of their graphs. Why does c(t)
have no vertical asymptotes? EXPLAIN HOW THIS FUNCTION COULD HAVE ASYMPTOTES,
IGNORE CONTEXT IF NECESSARY.
Find lim c(t). Explain your answer in the context of the problem.
е.
t→∞
Transcribed Image Text:Rational Functions: 3. 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 5t c(t) t2 + 1 Graphing this still help you here. may a. What is the highest concentration of drug that is reached in the patient's bloodstream? When would this approximately happen? b. How long does it take for the concentration to drop below 0.3 mg/L? c. Give the domain and range of this function, in context, using interval notation. d. Many rational functions have vertical asymptotes as a feature of their graphs. Why does c(t) have no vertical asymptotes? EXPLAIN HOW THIS FUNCTION COULD HAVE ASYMPTOTES, IGNORE CONTEXT IF NECESSARY. Find lim c(t). Explain your answer in the context of the problem. е. t→∞
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