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.

a. use the graph to obtain a reasonable estimate of the drugs concentration after 2 hours.
the drugs concentration after 2 hours is approximately 1.3 milligrams per liter.
(round to the nearest tenth as needed.)

b. use the functions equation to determine the drugs concentration after 2 hours.
the drugs concentration after 2 hours is \\( \square \\)
(round to the nearest tenth as needed.)

Explanation:

Step1: Substitute \(t = 2\) into the function

Given \(C(t)=\frac{4t}{t^{2}+2}\), when \(t = 2\), we have \(C(2)=\frac{4\times2}{2^{2}+2}\).

Step2: Simplify the expression

First, calculate the denominator \(2^{2}+2=4 + 2=6\), and the numerator \(4\times2 = 8\). So \(C(2)=\frac{8}{6}=\frac{4}{3}\approx1.3\) (rounded to the nearest tenth).

Answer:

\(1.3\)