### Question Description

Part A:

Let’s consider the US national debt and the US population as a function of time.

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 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:

Time (years) Debt ($) Population Debt/Citizen

0 17,000,000,000 317,000,000

10

20

30

Graph the function that shows the amount of debt per citizen as a function of time. 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). Identify the ordered pairs at x = 0, 10, 20 and 30 years either on

the graph or below it. Is this a linear function? Why or why not?

5. If the current compound interest rate on our national debt is 8% (compounded annually),

what will the national debt be in 5, 10, and 20 years? The current national debt is

$17,000,000,000. Show equations for all three calculations. Please find the exact values,do not round.

6. At what point does the compound interest on the national debt double the amount from

the current year? The current national debt is $17,000,000,000. Solve algebraically, and

show all of your work. Find the exact value. Assume the interest rate is 8% and the

interest rate is compounded annually.

Part B:

For this part, we will look at equations with two variables in a business setting. Suppose a company's profit was 15% lower in June than in May. The total profit for both months together is $32,375.

7. Find the profit for each month. Show all work and provide justifications or explanation for each step.

Part C:

The given quadratic equation:

y=x^2 +2x-3

Graph the quadratic equation

Label and include the ordered pair(S) for the x-intercepts on the graph

Provide the solution to the quadratic equation: x^2 +2x-3=0

## Final Answer

Hello, I have your answers.

Problem 1

Population

National Debt

317,000,000

$ 17,000,000,000.00

317,000,000x=17,000,000,000

x

$

Where x is the debt per citizen

53.63 per citizen

Problem 2

(1+0.009x)317,000,000=y

y=2,853,000x+317,000,000

(1+0.13x)17,000,000,000=y

y=2,210,000,000x+17,000,000,000

where x is the # of years and y is

the population in year x

where x is the # of years and y is

the debt in year x

Problem 3

y=2,210,000,000(30)+17,000,000,000

y=83,300,000,000

y=2,853,000(30)+317,000,000

y=402,590,000

Year

Debt in 30 years

Population in 30 years

x=83,300,000,000/402,590,000

x=$206.91

Debt per citizen in ...

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