Answer
a. After $x=3$ the graph approaches approximately $1.5$.
b. $C(3)=1.5$
c. $y=0$ (the horizontal asymptote)
Work Step by Step
a. From the graph we can approximate that the after $x=3$ the graph approaches approximately $1.5$.
b. $C(3)=\frac{5\times3}{3^2+1}=1.5$
c.
The rules of horizontal asymptotes for rational functions are as follows:
1. If the numerator's degree is less than the denominator's degree, there is a horizontal asymptote at $y = 0$.
2. If the numerator's degree equals the denominator's degree, there is a horizontal asymptote at $y = c$, where $c$ is the ratio of the leading terms or their coefficients.
3. If the numerator's degree is more than the denominator's degree, then there is no horizontal asymptote.
$C(t)=\frac{5t}{3t^2+1}$
Therefore, in this case the degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is $y=0$..
This means that as tine increases, the drugs concentration in the blood stream will approach $0$.
