Question

please help I am lost,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 C(t) = (5t/t^2+1)the graph of this rational function obtained with a graphing utility is shown in the figurey= (5x/x^2+1)[0,10,1] by [0,3,1]a. use the graph to obtain a reasonable estimate of the drugs concentration after 3 hours.b. use the functions equation displayed in the voice balloon by the graph to determine the drugs concentration after 3 hoursc. use the functions equation to find the horizontal asymptote for the graph. describe what this means about the drugs concentration in the patient's bloodstream as Time increases.

Answer 1

Explanation:

a)

Looking at the graph, it is reasonable to assume that after 3 hours, the concentration should be about 1.5 miligrams per liter.

b)

$\begin{gathered} We\text{ will subsitute t =3 into the equation:} \\ y\text{ = }\frac{5(3)}{3^2+1} \\ \text{ =1.5} \end{gathered}$

Answer: Concentration = 1.5 miligrams per liter after three hours.

c)

The function is given by a term in the numerator and a term in the denominator. The term in the denominator cannot equal 0.

$\begin{gathered} x^2+1\ne0 \\ But,\text{ x}^2\text{ will never be negative and the function cannot y cannot go below 0.} \end{gathered}$

Answer: The horizontal asymptote is the line y = 0