1RATIONAL FUNCTIONS IN MEDICINERational Functions in MedicineVirtual High School: OntarioAbstractMedicine is one of the most important professions nowadays because they try to save people life no matter what they have to do. It is common knowledge that math is very important for all professions including those in medicine, which uses multiple types of functions for many different situations. The main objective of this report will be to analyze how rational functions specifically are used to calculate the percentage of the concentration of medicine in our blood when patients are sick and doctors need to give medicine to allow the patient to feel better. For that an example in which this situation is modeled with a rational function and will be analyzed in a deeper way. With this, we can explain that math is useful for almost everything in the world and also on an important topic such as medicine. Key Words: Rational functions, medicine, prescriptions, bloodIntroductionMedicine is very important in a well-functioning society. “Medicine is the art of preventing or curing disease; the science concerned with disease in all its relations” (Nordqvist, 2012). We need multiple requirements for being a doctor, such as chemistry, biology, mathematics and humanities all of them at a high level. A daily basis of a doctor varies with the specialization they take in college. Medicine has a lot of specializations such as “anatomy, biochemistry, cytology, embryology, endocrinology, epidemiology, histology, microbiology, nutrition, etc. (There are many more)” (Nordqvist, 2012). No matter what doctors has a unique function: to help people and cure them. Daily, doctors see people and analyze their symptoms helping to cure them with drugs or with medical treatment. Doctors have many hectic days as they are trying to save lives, as since they need to take special care of every person they treat. The average salary of a doctor depends on the country in which they working. Countries such as Colombia undervalue the job of the doctors and the payment isn’t well for them. They have an average of C$14,500 in a year. Although other countries such as Canada or the U.S.A. The average salary is about C$307,000 according to the CIHI (Canadian Institute for Health Information) (CIHI, 2013). Math is used in a doctor’s career in many of ways, in this case, let’s specify in the prescriptions and medications “Regularly, doctors write prescriptions to their patients for various ailments. Prescriptions indicate a specific medication and dosage amount. Most medications have guidelines for dosage amounts in milligrams (mg) per kilogram (kg). Doctors need to figure out how many milligrams of medication each patient will need, depending on their weight” (University of Regina, 2011): For making this doctors would need to model rational functions and determine with a graph the amount of the medicine in respect to the height, weight and the time it will be in the blood of the patient. CalculationsOne example of this function applied to medicine is this one: The percentage of drug in a person’s bloodstream t hours after its injections is approximated by the function c(t)=5t/(4t^2+5). Approximately what percentage of the drug is in the person’s bloodstream after 5,5 hours? (HDSB, 2013). This is relevant to medicine because the drugs may be controlled when it is in a patient, so the function will control the amount of this medicine in respect to the time for the patient to be cured. The next step is to make all the calculations for determining a solution to the problem. x-intercepts: 5x=0 x=0, So the x-intercept will be the origin (0,0) y-intercept: f(0)=0, So the y-intercept will be also in the origin (0,0)As the degree of the numerator is lower than the degree of the denominator then the vertical asymptote will be in y= 0. It has no vertical asymptotes because, in any case, the denominator could be 0. This function has no holes because it cannot be factored. For this exercise, we will need the interval of the whole number (0,?) and the maximum value there is in y= 0.56, in this case, we don’t have a minimum value in this interval. The domain of the function is (0, ?) and the range will be (0, 0.56). With this information, we know that the maximum percentage in the blood will be of 56% if it is bigger the patient will have problems and maybe die. And also that when the drug is in the blood it will never go away because the asymptote is 0 so it will be approaching to 0 but never touch it.Before, it was said that the maximum represents the maximum percentage of a drug that could be in the blood without damage to the patients’ health if this maximum is exceeded the patients could suffer serious injuries or maybe death.As shown both graphs are similar so we can see that the sketch of the function is correct. For solving the problem we go to the point x=5.5 so the coordinate will be (5.5, 0.2183) so the amount will be 0.2183 multiplied by 100% which is 21.83%. This can be proved mathematically by replacing 5.5 in the equation.c5.5=5(5.5)4(5.5)2+5=27.5126=0.21825*100%=21.83%ConclusionConcluding, we can see that math is very important for medicine in the case for the prescriptions and the drugs amount in the blood. Also, we can conclude that there is a maximum value of the drug that can be applied in blood if this value is exceeded the patient will have a lot of problems with his health. On the other hand, we can see that as the time goes on the percentage of the drug in the blood will be less but it will never be zero, so we have to take care and only consume medicines when it is completely necessary. Rational functions help a tremendous amount in medicine and that is demonstrated with this example.