what’s your issue? cost of medical care vs. average salaries

What’s Your Issue?

Cost of Medical Care vs. Average Salaries

Jonathan Kuc

(2012). Health Care Costs: A Primer. In Kaiser Family Foundation. Retrieved from http://www.kff.org/

(2012). National Average Wage Index. In Social Security: The Official Website of the U.S. Social Security Administration. Retrieved from http://www.ssa.gov/

Year Average Salary Cost of Medical Care2000 32154 48782001 32921 52412002 33252 56872003 34064 61142004 35648 64882005 36952 68682006 38651 72512007 40405 76282008 41334 79112009 40711 8149

Cost of Medical Care vs. Average Salary


Piecewise Function:f(x)={32921<x<34064 36952<x<40711}

Year Average Salary ($)2000 321542001 329212002 332522003 340642004 356482005 369522006 386512007 404052008 413342009 407112010 416622011 426132012 435632013 445142014 45464

(2012). National Average Wage Index. In Social Security: The Official Website of the U.S. Social Security Administration. Retrieved from http://www.ssa.gov/

Average Salaries Projected 5 Years

1998 2000 2002 2004 2006 2008 2010 2012 2014 20160

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000


KnownExpected

Year

Ave

rage

Sal

arie

s ($

)

Equation of Trend Line: y=8557/9x-1869401.556


Trend Line Work:

Points on Line=(2000, 32154) (2009,40711)

Slope Intercept Form= (40711-32154)/(2009-2000) = 8557/9

32154=85557/9(2000)+b

y=8557/9x-y=8557/9x-1869401.556


Year Cost of Medical Care ($)2000 48782001 52412002 56872003 61142004 64882005 68682006 72512007 76282008 79112009 81492010 85122011 88762012 92392013 96032014 9966


Cost of Medical Care Projected 5 Years

1998 2000 2002 2004 2006 2008 2010 2012 2014 20160

2000

4000

6000

8000

10000

12000


KnownExpected

Year

Cos

t of

Med

ical

Car

e ($

)


Equation of Trend Line: y=3271/9x-722010.888

Trend Line Work:

Points on Line=(2000, 32154) (2009,40711)

Slope Intercept Form= (40711-32154)/(2009-2000) = 8557/9

32154=85557/9(2000)+b

y=8557/9x-1869401.888

Cost of Medical CareProjected 5 Years

Quadratic A Function

1)Three Points: (34064,6114)

(33252,5687)

(32921,5241)

2a) Vertex Form:

Vertex Point: (34064,6114) | Other Point: (33252,5687)

i. f(x)=a(x-34064)2+6114

ii. 5687=a(33252-34064)2+6114

iii. -427=659344a

iv. a=-0.00065

v. f(x)=-0.00065(x-34064)2+6114


2a) General Form:

i. f(x)=-0.00065(x-34064)2+6114

ii. -0.00065(x-34064) (x-34064) +6114

iii. -0.00065(x2-68128x+1160356096)+6114

iv. -0.00065x2+44.2832x-754231.4624+6114

v. f(x)= -0.00065x2+44.2832x-748117.4624

2b) f(x)=a(x-h)2+k

i) The f(x) and x in the vertex form are the x and y coordinates of one of the three points were chosen.

ii)The h and k in the vertex form are the x and y coordinates of another one of the three points chosen such as (34064, 6114).

iii)The a is the leading coefficient that determines concavity.


2c) The concavity of this graph is down because the leading coefficient is a negative number. Also, on the actual graph the parabola is facing downwards.

2d) Maximum Point (34064,6114)

2e) –(44.2832)/ 2(-0.00065) = 34064

2f) i. f(x)=-0.00065(34064) 2+44.2832(34064)-748117.4624

ii. 6114

iii. (34064,6114)

2g) X Intercept

X= {30997.05464, 37130.94536}

30997.0546437130.94536


2g) Y Intercept

i. f(x)=-0.00065x2+44.2832x-748117.4624

ii. f(x)=-0.00065(0)2+44.2832(0)-748117.4624

iii. f(x)=-748117.4624

Y={-748117.4624 }

2h) f(x)=ax2+bx+c

i) The ax2 is the quadratic part of the equation.

ii)The bx is the linear part of the equation.

iii)The c is the constant of the equation.

2i) No solutions can be found through grouping or reverse foil because there are three terms and the leading coefficient is a number that will not allow for solutions to be found.


2j) X Intercept

X= {30997.05464, 37130.94536}

2j) There are two real solutions which are 30997.05464 and 37130.94536.

2l) The solutions are real because they came from a quadratic that have a positive number under the radical which means that it real. Also, if the lines on the graph were extended then they would hit the x axis at one point. Overall, there is no “I” in the two solutions, which means that these solutions are real.

30997.0546437130.94536


2n) i. 5241=-0.00065(32921) 2+44.832(32921)-748117.4624

ii. 5241=-704464.9567+1457847.227-748117.4624

iii. 5241=5241

3a) The effect on my data would be:

-The parabola flips my data making the actual parabola open up opposed to opening down:

-This would happen because the costs would start out high and then gradually as the income increases the prices lower until they hit a point where they are affordable but stop decreasing

-Then, the prices would continue to increase as the incomes increase


3b) The effect on my data would be:

-The parabola shifts down several units:

-This can be caused by the medical services essentially becoming free to everyone so there would be no cost for it

-Also, the cost decreased and the costs cannot go into the negative numbers because it is unreasonable to have a negative cost.

Quadratic B Function

1)Three Points: (38651,7251)

(40405,7628)

(40711,8149)

2a) Vertex Form:

Vertex Point: (38651,7251) | Other Point: (40405,7628)

i. f(x)=a(x-38651)2+7251

ii. 7628=a(40405-34064)2+6114

iii. 377=3076516a

iv. a=0.00012

v. f(x)=0.00012(x-38651)2+7251

2a) General Form:

i. f(x)=0.00012(x-38651)2+7251

ii. 0.00012(x-38651)(x-38651) +7251

iii. 0.00012(x2-77302x+1493899801)+7251

iv. 0.00012x2-9.27624x+179267.9761+7251

v. f(x)= 0.00012x2-9.27624x+186518.97612

2b) f(x)=a(x-h)2+k

i) The f(x) and x in the vertex form are the x and y coordinates of one of the three points were chosen.

ii)The h and k in the vertex form are the x and y coordinates of another one of the three points chosen such as (38651, 7251).

iii)The a is the leading coefficient that determines concavity.



2c) The concavity of this graph is up because the leading coefficient is a positive number. Also, on the actual graph the parabola is facing upwards.

2d) Minimum Point (38651,7251)

2e) –(-9.27624)/ 2(0.00012) = 38651

2f) i. f(x)=0.00012(38651) 2-9.27624(38651) +186518.97612

ii. 7251

iii. (38651,7251)

2g) X Intercept

X= {46424.35192i, 30877.64808i}

46424.35192i30877.64808i


2g) Y Intercept

i. f(x)= 0.00012x2-9.27624x+186518.97612

ii. f(x)=0.00012(0)2-9.27624(0) +186518.97612

iii. f(x)=186518.97612

Y={186518.97612}

2h) f(x)=ax2+bx+c

i) The ax2 is the quadratic part of the equation.

ii)The bx is the linear part of the equation.

iii)The c is the constant of the equation.

2i) No solutions can be found through grouping or reverse foil because there are three terms and the leading coefficient is a number that will not allow for solutions to be found.


2j) X Intercept

X= {46424.35192i, 30877.64808i}

2j) There are no real solutions but there are two imaginary solutions that are 30997.05464 and 37130.94536.

2l) The solutions are imaginary because they came from a quadratic that have a negative number under the radical which means that it is imaginary. Also, if the lines on the graph were extended then they would never hit the x axis. Overall, there is an “I” in the two solutions, which means that these solutions are imaginary.

46424.35192i30877.64808i


2n) i. 8149=0.00012(40711) 2-9.27624(40711)+186518.97612

ii. 8149198886.2625-377645.0066+186518.97612

iii. 8149=8149

3a) The effect on my data would be:

-Make parabola a little more narrow and shift down a few units:

-This could be caused by the costs starting out very high -But as the incomes rose the price dropped at a

significant rate until it was affordable for a short while

-However, the cost increased at a quick rate after a little while because of the incomes rising again.


3b) The effect on my parabola would be:

-The parabola would be shifted down several units:

-This could be caused by the cost of medical care started up high

-But as the incomes increased the medical care became free at some point

-Although it was free briefly, the prices continued to increase after a little while and the incomes

increased as well

Data Comparison

4a)


0 5 10 15 20 25 30 35 40 45 500

1

2

3

4

5

6

7

8

Figure 1: National Health Expeditures per Capita 1960-2010

Years After 1960

Cos

t of

Med

ical

Car

e ($

)(i

n t

hou

san

ds)

Equation of Trend Line: y=1.247/3x-48253/10000General Form: f(x)=-0.01074074074x2+0.46937037037x+4.78237037037Vertex Form: -0.01074074074(x-21.8500000015)2-0.34550092627

Trend Line Work:

Points on Line=(1, 5.241) (4,6.488)

Slope Intercept Form= (6.488-5.241)/(4-1) = 1.247/3

5.241= 1.247/3(1)+b

y=1.247/3x+4.8253

General Form:

1)Three Points: (38651,7251)

(40405,7628)

(40711,8149)

Continued…

Data Comparison

General Form:

i. 5.241=a(1)2+b(1)+c 5.241=1a+1b+c

ii. 6.488=a(4) 2+b(4)+c 6.488=16a+4b+c

iii. 8.402=a(10) 2+b(10)+c 8.402=100a+10b+c

a=-0.01074074074 b=0.46937037037 c=4.78237037037

f(x)=-0.01074074074x2+0.46937037037x+4.78237037037

Vertex Form:

i. f(x)=-0.01074074074x2+0.46937037037x+4.78237037037

ii. 0.01074074074(x2-43.700000003x+477.422500066)-0.34550092627

iii. -0.01074074074(x-21.8500000015)2-0.34550092627

Data Comparison

4b)There are a few differences and similarities in the equation of the trend lines of section 3 and section 4:-All the lines have a positive slope on the trend line-Trend lines also all points in the same direction-However, the graphs had different values for the slopes and for the y intercepts. Reasons for similarities: -The direction of the trend line are as a result of the positive correlation of the dataReasons for differences:

-The x and y values are different, which is the reason for the different slopes-Different y intercepts are a result of each graph having different x values such as years and years after 1960

Data Comparison

• The cost of medical care has been growing at a quicker rate than the average incomes of people.

• The process in which the data for average salaries and cost of medical was acquired was through several trusted and reliable websites such as Social Security and Kaiser Family Foundation’s website.

• It appears that the rate at which incomes are rising and the cost of medical care is rising at a very quick rate. The cost appears to be rising much quicker than the annual incomes of people.

• As a result, people must pay a higher percentage of their income for medical care, leading to a number of negative effects.

Abstract

Causes:• Cost of medical care is growing quickly every year because of

the increasing costs of medication and the new advance technology in hospitals.

• Incomes are growing at slower rate than medical care and this will cause families to not be able to keep up with the costs of medical care making it unaffordable for them.

• Many people are turning away from medical care and turning towards cheap alternatives like home remedies.

Causes of Issue

Effects:• Decrease in the amount of people that purchase health care

because it would create a financial burden for them.• Families less likely to spend money on medical care because a

limited budget might only allow for necessities in life like food and clothes.

• Companies are raising prices to make up for all the money they lost from customers who left.

Effects of Issue

what’s your issue? cost of medical care vs. average salaries

Documents

health care costs

average salary2

average salaries whats

average salariesjonathan

national average wage

kaiser family foundation

social security administration

official website