Question

A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams after t hours is modeled by $C(t) = \frac{8t}{3t^2 + 3}$. What is the horizontal asymptote for this function? Describe what this means in practical terms. A. y=2.67; After 2.67 hours, the concentration of the drug is at its greatest. B. y=1.33; After 1.33 hours, the concentration of the drug is at its greatest. C. y=0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream. D. y=2.67; 2.67 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.

          A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams after t hours is modeled by $C(t) = \frac{8t}{3t^2 + 3}$. What is the horizontal asymptote for this function? Describe what this means in practical terms.
A. y=2.67; After 2.67 hours, the concentration of the drug is at its greatest.
B. y=1.33; After 1.33 hours, the concentration of the drug is at its greatest.
C. y=0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.
D. y=2.67; 2.67 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.

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A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams after t hours is modeled by C(t) = (8t)/(3t^2 + 3). What is the horizontal asymptote for this function? Describe what this means in practical terms.
A. y=2.67; After 2.67 hours, the concentration of the drug is at its greatest.
B. y=1.33; After 1.33 hours, the concentration of the drug is at its greatest.
C. y=0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.
D. y=2.67; 2.67 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.

Added by Monica M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Marcella Sippey

08/16/2023

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This is a rational function, where the numerator is a linear function (8t) and the denominator is a quadratic function (3t^2 + 3). Show more…

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A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams after t hours is modeled by C(t)=(8t)/(3t^(2)+3). What is the horizontal asymptote for this function? Describe what this means in practical terms. q, A. y=2.67; After 2.67 hours, the concentration of the drug is at its greatest. B. y=1.33; After 1.33 hours, the concentration of the drug is at its greatest. C. y=0;0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream. D. y=2.67;2.67 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream. A drug is injected into a patient and the concentration of the drug is monitored.The drugs concentration Ct,in milligrams after t hours is modeled by Ct= 8t means in practical terms. 32+3 .What is the horizontal asymptote for this functionDescribe what this O A.y=2.67; After 2.67 hours,the concentration of the drug is at its greatest O B.y=1.33; After 1.33 hours, the concentration of the drug is at its greatest. O C.y=O;0 is the final amount,in milligrams,of the drug that will be left in the patient's bloodstream OD.y=2.67;2.67 is the final amount,in milligrams,of the drug that will be left in the patient's bloodstream.

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Transcript

00:01 All right, i brought the graph over because they're asking you to identify, i'll get the wording here, use the graph to obtain a reasonable estimate of the drugs concentration after three hours.

00:12 So they're telling you that the scaling here is zero to 10, so that makes this bottom by ones zero to 10, and then the y -axis zero to three by one.

00:24 So if i want three hours, i go one, see if i can actually type in there, there we go, one, two, three is going to be here.

00:32 So then i just kind of come up and that looks like that's a two.

00:36 So the graph shows that that concentration of drugs is two, and then what do they label that in? milligrams per liter, milligrams per liter.

00:48 Then they ask you to use the function's equation, which they're calling c of t equals eight t over t squared plus three after three hours.

00:59 So that just means you're putting three in for t.

01:06 So eight times three is 24, three squared is nine, nine plus three is 12, and of course 12 over, i lied, 24 over 12 is two.

01:15 So they're using that graph and you did it algebraically and you got the exact same answer.

01:21 Then the third question asks you to identify what the horizontal asymmethod is.

01:27 So if we know anything about horizontal asymmethods, you have to look at the degree of the numerator and the degree of the denominator.

01:34 If the degree of the numerator is less than the degree of the denominator, then you have a horizontal asymptote at y equals zero...

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