# Algebra question with Linear Equations and Graph

**Question description**

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 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:

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%.

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