Dr. Rational

           In this Desmos activity the main topic was rational functions. It used the concentration of medicine in the bloodstream as away to show how this topic could be used in a real world setting. The way rational functions are used in medicine is to figure out how much time the surgeon would need to wait for the medicine to kick in order to conduct the surgery on the patient.  I will use two functions That’ve selected to demonstrate the types of rational functions that are used.
    I will first start off this blog post with the definition of horizontal asymptotes. Which are horizontal lines at a function will approach as x tends to +∞ or −∞ on a graph. Now
in this example the drugs apparently require me to reduce the concentration of medicine to 0.4 milligrams/liter. With the two functions I have chosen. One will correctly tell me how the surgeon would need to wait before conducting the surgery. While the other wouldn’t be correct.
g(x ) = 12x/4x^2-9 and h(x) = 9/x^2+1
x = 0.4 milligrams/liter
g(x ) = 12x/4x^2-9                     h(x) = 9/x^2+1
g(0.4) = 12(0.4)/4(0.4)^2-9        h(0.4) = 9/(0.4)^2+1
g(0.4) = 4.8/0.16-9                      h(0.4) = 9/0.16+1
g(0.4) = 4.8/-8.84                         h(0.4) = 9/1.16
g(0.4) = -0.574162679426          h(0.4) = 7.75862068966
g(0.4) = -0.6 min.                       h(0.4) = 7.8 min.
As you can see with the function g(x) gives a negative amount of minutes to wait for the medicine to travel the blood stream. That obviously doesn’t make sense. The only function that does make sense is h(x), because it gives a positive solution to the number of minutes the concentration of medicine takes to cycle the bloodstream. As for horizontal asymptope as time passes the doses of medicine will get close to the horizontal asymptote, but will never completely touch it. So in theory, the medicine would never leave the patients blood stream completely.
Could anyone figure out a example that could work with rational functions?
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