hat 20mg have been washed out and only 30mg remain in the body. The patient continues to take their 50mg pill each morning. This means that on the morning of day two, the patient has the 30mg left over from day one, as well as another 50mg from the morning of day two, which is a total of 80mg. As this continues, doctors must determine how often a patient needs to take their medication, and for how long, in order to keep enough medicine in the patient’s body to work effectively, but without overdosing.
The amount of medicine in the body after taking a medication decreases by a certain percentage in a certain time (perhaps 10% each hour, for example). This percentage decrease can be expressed as a rational number, 1/10. Hence in each hour, if the amount at the end of the hour decreases by 1/10 then the amount remaining is 9/10 of the amount at the beginning of the hour. This constant rational decrease creates a geometric sequence. So, if a patient takes a pill that has 200mg of a certain drug, the decrease of medication in their body each hour can be seen in the folowing table. The Start column contains the number of mg of the drug remaining in the system at the start of the hour and the End column contains the number of mg of the drug remaining in the system at the end of the hour.
||9/10 x 200 = 180
||9/10 x 180 = 162
||9/10 x 162 = 145.8
The sequence of numbers shown above is geometric because there is a common ratio between terms, in this case 9/10. Doctors can use this idea to quickly decide how often a patient needs to take their prescribed medication.
Ratios and Proportions
Nurses also use ratios and proportions when administering medication. Nurses need to know how much medicine a patient needs depending on their weight. Nurses need to be able to understand the doctor’s orders. Such an order may be given as: 25 mcg/kg/min. If the patient weighs 52kg, how many milligrams should the patient receive in one hour? In order to do this, nurses must convert micrograms (mcg) to milligrams (mg). If 1mcg = 0.001mg, we can find the amount (in mg) of 25mcg by setting up a proportion.
By cross-multiplying and dividing, we see that 25mcg = 0.025mg. If the patient weighs 52kg, then the patient receives 0.025(52) = 1.3mg per minute. There are 60 minutes in an hour, so in one hour the patient should receive
1.3(60) = 78mg. Nurses use ratios and proportions daily, as well as converting important units. They have special “shortcuts” they use to do this math accurately and efficiently in a short amount of time.
Numbers give doctors much information about a patient’s condition. White blood cell counts are generally given as a numerical value between 4 and 10. However, a count of 7.2 actually means that there are 7200 white blood cells in each drop of blood (about a microlitre). In much the same way, the measure of creatinine (a measure of kidney function) in a blood sample is given as X mg per deciliter of blood. Doctors need to know that a measure of 1.3 could mean some extent of kidney failure. Numbers help doctors understand a patient’s condition. They provide measurements of health, which can be warning signs of infection, illness, or disease.
Body Mass Index
In terms of medicine and health, a person’s Body Mass Index (BMI) is a useful measure. Your BMI is equal to your weight in pounds, times 704.7, divided by the square of your height in inches. This method is not always accurate for people with very high muscle mass because the weight of muscle is greater than the weight of fat. In this case, the calculated BMI measurement may be misleading. There are special machines that find a person’s BMI. We can find the BMI of a 145-pound woman who is 5’6” tall as follows.
First, we need to convert the height measurement of 5’6” into inches, which is 66”. Then, the woman’s BMI would be:
This is a normal Body Mass Index. A normal BMI is less than 25. A BMI between 25 and 29.9 is considered to be overweight and a BMI greater than 30 is considered to be obese. BMI measurements give doctors information about a patient’s health. Doctor’s can use