Megha P. answered • 04/18/15
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"The Linear equation for the population in slope-intercept form. "
To find out slope for this equation, we would need to derive two points of the linear equation. We always take the current year as a 0th year. And we know at 0th-year population is 317,000,000
After a year population will be raised by 0.9% to 319,853,000. Base on this information we can derive the following two points.
X Y
0 317,000,000
1 319,853,000
The slope for these two point is 2,853,000 and Y intercept is 317,000,000.
Base on this information we can derive an equation. Y= (slope)2,853,000X + 317,000,000.
Following the same procedure we can derive a linear equation for debt too. If you find trouble solving it let me know.
Adrian R.
1. The current population of the United States is 317,000,000.
The current national debt total is $17,000,000,000.
Based on these figures, use algebraic equations to calculate the approximate amount of
debt per citizen. Show all of your work.
2. For the purposes of this project, assume that population growth is a linear function that
grows at a steady, unchanging rate of 0.9% per year, and that debt growth is a linear
function that grows at a steady, unchanging rate of 13% per year.
Use the population and debt figures from #1. Show all of your work.
Find the linear equation for population in slope-intercept form.
Find the linear equation for debt in slope-intercept form.
3. Graph the linear equation for population growth and debt in separate graphs. Label the
values of the x- and y-axes and title the graph. Show x from 0 (current year) to 30 (30
years from now). Determine what the population and national debt will be 30 years from
now. Calculate what the debt per citizen will be in 30 years. Show all of your work.
4. Using calculations from #1 and # 3, calculate the population, national debt, and debt per
citizen in 10 and 20 years from now. Complete the table below with your calculations.
Please be sure to show all work needed to complete the calculations:
Debt = $17,000,000,000
Population = 317,000,000
Equation: $17,000,000,000/317,000,000
Therefore, the approximate debt per citizen will be $53,627.76
2. Slope Intercept Equation for population:
0.9(#of years) + population = growth which will be 9/10x+317=y
Slope Intercept Equation for Debt
0.13(# of years) + debt = growth = 13/100x +17 = y
3. Population in 30 years = 344 million
National Debt in 30 years = 20.9 trillion
Debt per citizen in 30 years = $60,753.81
4. F(30)=0.13x +17/g(30)=0.9x +317
Debt over population in 20 years = 19.6/35
Debt per citizen in 20 years = $58,507.46
X y
0 53,627.76
10 53,696.76
20 53,765.76
The graph is a linear function because there is not sufficient data accumulated to produce a non linear function.
5. 5 years = 17(1*0.08/1)^(1)5 = 25 trillion
10 years = 17(1*0.08/1)^(1)10=36.7 trillion
20 years = 17(1*0.08/1)^(1)20=78.25 trillion
6. 17(1*0.08/1)^y=19.72
Therefore, during the first year, the debt will accrue 1.36 trillion dollars of interest
17(1*0.08/1)^y=19.72
As a result, it will take about 1.93 years to double the expense of the first year
04/18/15