Question

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Explanation:

Step1: Understand the function's input and output

The function \(C(t)=\frac{4t}{t^{2}+2}\) gives the drug concentration \(C(t)\) (in milligrams per liter) at time \(t\) (in hours).

Step2: Substitute \(t = 2\) into the function

When \(t = 2\), we calculate \(C(2)=\frac{4\times2}{2^{2}+2}\).
First, compute the denominator: \(2^{2}+2=4 + 2=6\).
Then, compute the numerator: \(4\times2 = 8\).
So, \(C(2)=\frac{8}{6}=\frac{4}{3}\approx1.3\).

Answer:

The drug's concentration after 2 hours is approximately \(1.3\) milligrams per liter.