4. An athlete can burn 9 calories per minute on a stationary
bicycle,
11.5 calories per minute on a stair climber
The total amount of exercise is 30 minutes
In the 30 minute workout the athlete burns 300 calories
◦ How many minutes does the athlete spend on each type of
exercise equipment?
5. x=(9) the number of min. on stationary bike
y=(11.5) the number of min. on stair climber
x + y =30 (total workout time)
9x + 11.5y = 300 (calories burned)
-----------------------------------------------------
x + y = 30 (multiply by -9)
-9x -9y = -270
9x + 11.5y = 300
_____________________________________________________________
2.5y = 30
y= 12 minutes on stair climber, therefore
x= 18 minutes on bicycle
30 total minutes on equipment
y= 12 x 11.5 = 138 ; x = 18 x 9 = 162: Total Calories=300
6. Maximum heart rate
◦ R = 220-A
◦ A= Persons age
◦ B= Beats per minute
◦ (a) Find heart rate for a 20 yr. old and 70 yr. old
◦ (b) sketch a graph of R≤ 220-A
◦ (c) Interpret the graph
220- 20= 200 bpm for a 20 year old person
220- 70 = 150 bpm for a 70 year old person
12. Fat Grams: A cup of milk contains 8 grams of fat.
(a) Give a formula for f(x) that calculates the number of
fat grams in x cups of milk.
a) f (x) = 8x
(b) What is the slope of the graph of f ?
b) m=8
(c) Interpret the slope as a rate of change.
c) As the number of cups increase by one, the
amount of fat increases by 8 grams.
15. Target Heart Rate: A target heart rate T that is 70%
of a person’s maximum heart rate is approximated by
T=150-0.7A where A is a persons age.
(a)What is T for a person 20 years old? 60 years old?
T= 150-0.7 (20) T=136
T=150-0.7 (60) T=108
16. (Age, THR)
(20, 136)
(30, 129)
(40, 122)
(50, 115)
(60, 108)
(b) Sketch a graph of T ( is greater than or equal to)
150-0.7 A. Assume that A is between 20 and 60.
(c) Interpret this graph.
18. Chlorine In Swimming Pools
Initially the pool has chlorine of 3 parts per million
20% dissipates daily
No additional chlorine is added.
19. Day 1- 3ppm x .80 =2.4 ppm
Day 2- 2.4 ppm X.80 = 1.92 ppm
Day 3- 1.92 ppm x 0.80= 1.536 ppm
Day 4- 1.536ppm x 0.80= 1.228 ppm
This is a geometric sequence with a common ratio of
0.80
The first four terms are: 2.4, 1.92, 1.536 and 1.228.
Successive terms are found by multiplying the previous
term by 0.80
Rockswold & Krieger, (2009)
20.
21. Air Filtration
Each air filter removes 80% of the impurities.
How many filters are needed to remove 96% of
impurities?
24. Heart Rate of an Athlete running a 100- meter
race. The race last 10 seconds.
A.) Does P(t)=0.2(t)2+5t+90 model the data in the
table exactly?
P(0)=0.2(0)2+5(0)+90=90
25.
26. The following table list the calories burned by a 140-pound
person walking at 4 miles per hour for various lengths of
times.
29. http://www.chinadaily.com.cn/english/doc/2005-05/13/content_441834.htm
McKinley Health Center, (2008). University of Illinois at Urbana-
Champaign-Macronutrients: the Importance of Carbohydrate,
Protein, and Fat. Retrieved on August 2, 2011 from http://www.mckinley.
illinois.edu/Handouts/macronutrients.htm
Rockswold, G.K. & Krieger, T.A.(2009). Beginning and intermediate
algebra with applications and visualization. (2nd ed.). Boston, MA:
Addison – Wesley
http://www.smartmotorist.com/traffic-and-safety-guideline/what-causes-
car-accidents.html
Editor's Notes
Thank you for attending this presentation. The goal of this lecture is to become aware of how healthcare professionals can combine efforts of math and science to reach the pinnacle of financial productivity in this unsteady time in healthcare.
Sustainability is a balance or homeostasis of the body while pushing it just enough to continue to reach the objective. We must maintain the balance in the art of guiding our clients or patients in their journey to become healthy. We will show how to reach these goals by having a plan and using the algebraic tools to get the necessary results. We must first have reasonable, measurable goals for the client. In having measurable goals, then the client will be encouraged by seeing the results. By seeing the results we will have satisfied clients which will lead to more clients and more profit.
When you are creating the individualized plan for your client, you must figure what will be the best exercises to reach the anticipated goals. Create a nutritional plan with enough calories and macronutrients to sustain the client while performing the necessary exercises.
A system of linear equation can be used to determine the amount of time that the athlete spends on each type of equipment.
To solve this equation the first step is to identify each variable, within this exercise the variables are the number of minutes on the stationary bike, and the number of minutes on the stair climber. The second step of the linear equation is to write a system of equations. The third step; solve the linear equation by eliminating one of the variables. The final step is to check the answer.
To calculate the maximum heart rate(beats per minute), simply take the persons age and subtract it from 220.
This graph represents possible heart rates for a person between the ages of 20 and 70 years old.
Lung cancer and motor vehicle accidents are major issues for today. We must educate our clients in the potential dangers and the statistics of the data.
There were 104,5000 new cases of lung cancer for men. There were 84,000 new cases of lung cancer for women. The international medical field has linked smoking with cancer since the 1930s. But people completely neglected the discovery until the 1990s. Today, among all cancers, lung cancer ranks No 1 for men in both incidence and death rate. Although it ranks number two among all types of cancer in incidence for women, it is also the most deadly among all cancers for women. While most men with lung cancer smoke, most women develop lung cancer because of second-hand smoke. It is said the second-hand smoke contains more incompletely burnt matter, which in fact contains more cancer-causing substances. Therefore, even if you don't smoke, those smoking around you are putting you at a higher risk than themselves for developing lung cancer.
The number of motor vehicle deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years. Note that the number of motor vehicles on the road in creased from 1 million to 230 million between 1912 and 2003. What Causes Car Accidents? The dictionary defines accident as "an unexpected and undesirable event, a mishap unforeseen and without apparent cause." Strictly speaking, most accidents are not accidents at all: they are collisions that could and should have been avoided. So, what causes them, and how can you avoid them? Four factors contribute to the vast majority of collisions. In ascending order they are: Equipment Failure Roadway Design Poor Roadway Maintenance Driver Behavior Over 95% of motor vehicle accidents (MVAs, in the USA, or Road Traffic Accidents, RTAs, in Europe) involve some degree of driver behavior combined with one of the other three factors. Drivers always try to blame road conditions, equipment failure, or other drivers for those accidents. When the facts are truthfully presented, however, the behavior of the implicated driver is usually the primary cause. Most are caused by excessive speed or aggressive driver behavior
By using the tool of functions we can calculate the fat content of various foods.
In relation to a nutritionist, this exercise may be used to determine the amount of milk a patient needs to consume in order to maintain a healthy fat equilibrium in the body. Some fat is good for the human body and provides for: Normal growth and development Energy (fat is the most concentrated source of energy) Absorbing certain vitamins ( like vitamins A, D, E, K, and carotenoids) Providing cushioning for the organs Maintaining cell membranes Providing taste, consistency, and stability to foods
Please see slide for graph. This graph indicates the slope of fat grams per cup of milk. 1 Cup Milk = 8 grams/fat 2 Cups Milk = 16 grams/fat 3 Cups Milk = 24 grams/fat *The exercise did not indicate a specific type of milk; eg Non-fat,1%, 2%, or Regular.
The healthcare professional must be aware of the target heart rate per individual.
The target heart rate for a 20 year old is 136 beats per minute. The target heart rate for a 60 year old is 108 beats per minute. This data is THR 70% based on the textbook instruction of a maximum heart rate of 150 beats per minute.
(c) This graph portrays the target heart rate that is 70% of a person’s maximum heart rate between the ages of 20 and 60. The shaded area of the graph shows the possible heart rate for each age above 70%. I believe the only problem with the graph is that it does not mark the maximum heart rate for each age. *As the age increases the target heart rate decreases, so they are inversely proportional. In relation to a Physical Therapist, this exercise may be used when training patients; especially in cardio exercise.
These concepts will prove how one can calculate the chlorine content and the filtration rate of air filters. With more and more of the population having allergic reactions we must incorporate the data into our system. To gauge the rate of dispersion of chemicals in the pool and filtration rates, we utilize algebra formulas.
Let us look at this chlorine content of a swimming pool. We start with 3 ppm, 20% dissipates daily and no additional chlorine is added to the pool. We want to find a general term for the sequence that gives the chlorine content each day and give a graphical representation of the data.
We begin the solution by arranging our information into usable data. We see that we start with 3ppm chlorine content. If 20% of chlorine dissipates daily, that leaves 80% remaining in the water. To find the next day’s result we must multiply the previous day’s term by 0.80( which is the 80% chlorine left in the water) and each successive day is multiplied by the previous day’s result, so this is a geometric sequence, as stated by Rockswold & Krieger(2009).
As per the chart, the chlorine content decreases daily in parts per million Day 1- 3ppm x .80 =2.4 ppm Day 2- 2.4 ppm X.80 = 1.92 ppm Day 3- 1.92 ppm x 0.80= 1.536 ppm Day 4- 1.536ppm x 0.80= 1.228 ppm We have a geometric sequence.
We know that each filter will remove 80% of the impurities that pass through the filter. The first filter will trap 80%, the second traps 16 5 so we will need 2 filters.
The first filter traps 80% and the second filter will trap 80% 0f that filter which is 16% so we will need 2 filters to trap 96% of the impurities.
To care for the client we must calculate the heart rate at the end of exercise and how quickly they will recover.
We can observe from this graph the time and effect of rest when the client is cooling down.
A.) Would it be reasonable to assume that the point (0,0) could be included in the table? B.) What type of polynomial function would model these data? C.) Find a function C that models the calories burned in t minutes?
The graph shows the calories burned in correlation to the time exercised.
Sustainability has becomes an imperative for the healthcare field. This also includes hospitals, health care systems, clinics, health insurance providers, pharmaceutical and biotechnology firms, as well as medical equipment companies. It has a large social responsibility and sustainability issues. As health care organizations move forward with sustainability business practices, common organizational commitments each share include corporate governance, compliance, and transparency with transparent reporting of environmental, social, and economic sustainability practices. There are many issues to deal with in the health care system. People are constantly trying to figure out how to feel better, look better and take care of themselves and their families. Certain health issues are a concern, as people are learning more about health issues such as Diabetes, Cancer, diet and exercise, cholesterol and Cardiac issues, to name a few. Millions of dollars each year are spent on healthcare, and healthcare teaching. Large hospitals such as Kaiser have classes to teach those with health issues such as obesity, stress and wellness, and how to take better care of themselves. Physicians, nurses, physical and occupational therapists, dieticians and psychologists are just several of the staff members highly trained to teach people how to take better care of themselves. Healthcare is expensive although well worth it. A healthier person his more productive at home, work and in the community. The better people are trained to take better care of themselves, the healthier the community we have and the lower the cost of health care issues in the future.
