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) = (4t)/(t² + 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 (round to the nearest tenth as needed.)

Explanation:

Step1: Analyze the graph

The x - axis represents time \(t\) (in hours) and the y - axis represents the drug concentration \(C(t)\) (in milligrams per liter). We need to find the value of \(y\) when \(x = 2\).

Step2: Estimate from the graph

Looking at the graph with the domain \([0,10,1]\) (x - axis: from \(0\) to \(10\) with a tick every \(1\) unit) and range \([0,3,1]\) (y - axis: from \(0\) to \(3\) with a tick every \(1\) unit), when \(t = 2\), we can estimate the value of \(C(2)\).

Another way (using the formula \(C(t)=\frac{4t}{t^{2}+2}\)):
Substitute \(t = 2\) into the formula \(C(t)=\frac{4t}{t^{2}+2}\).

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Answer:

\(1.3\)