Question

a drug is injected into a patient and the concentration of the drug in the bloodstream is monitored. the drugs concentration, c(t), in milligrams per liter, after t hours is modeled by the equation below. the graph of this rational function is shown to the right. c(t) = \frac{4t}{t^2 + 2} complete parts a through c below. b. use the functions equation to determine the drugs concentration after 2 hours. the drugs concentration after 2 hours is 1.3 milligrams per liter. (round to the nearest tenth as needed.) c. use the functions equation, c(t) = \frac{4t}{t^2 + 2}, to find the horizontal asymptote for the graph. describe what this means about the drugs concentration in the patients bloodstream as time increases. select the correct choice below and, if necessary, fill in the answer box to complete your answer. a. the horizontal asymptote is y = 0. (type an equation.) b. there is no horizontal asymptote. which statement below best describes what the horizontal asymptote means? a. over time, the drugs concentration will approach 0 milligrams per liter. b. over time, the drugs concentration will slowly approach and then eventually reach 0 milligrams per liter. c. over time, the drugs concentration will reach 0 milligrams per liter. d. there is no horizontal asymptote.

Explanation:

Step1: Find the horizontal asymptote

For a rational function \(y = \frac{f(t)}{g(t)}\) where \(f(t)=4t\) (degree \(n = 1\)) and \(g(t)=t^{2}+2\) (degree \(m = 2\)).
When \(n

Step2: Interpret the horizontal asymptote

A horizontal asymptote \(y = 0\) for the function \(C(t)=\frac{4t}{t^{2}+2}\) means that as \(t\) (time) gets larger and larger (\(t
ightarrow\infty\)), the value of \(C(t)\) approaches \(0\).

Answer:

A. The horizontal asymptote is \(y = 0\).
A. Over time, the drug's concentration will approach 0 milligrams per liter.