# Algebra Word Problem 12

Let’s consider the US national debt and theUS population as a function of time. 1. The current population of the UnitedStates is 317,000,000. The current national debt total is \$17,000,000,000. Basedon these figures, use algebraic equations to calculate the approximate amountof debt per citizen. Show all of your work.

2. For the purposes of this project, assumethat population growth is a linear function that grows at a steady, unchangingrate of 0.9% per year, and that debt growth is a linear function that grows ata steady, unchanging rate of 13% per year. Use the population and debt figuresfrom #1. Show all of your work. Find the linear equation for population inslope-intercept form. Find the linear equation for debt in slope-interceptform.

3. Graph the linear equation for populationgrowth and debt in separate graphs. Label the values of the x- and y-axes andtitle 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 20years from now. Complete the table below with your calculations. Please be sureto show all work needed to complete the calculations:

Graph the function that shows the amount ofdebt per citizen as a function of time. Label the values of the x- and y-axesand 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 orbelow it. Is this a linear function? Why or why not?

5. If the current compound interest rate onour national debt is 8% (compounded annually), what will the national debt bein 5, 10, and 20 years? The current national debt is \$17,000,000,000. Showequations for all three calculations. Please find the exact values; do notround.

6. At what point does the compound intereston the national debt double the amount from the current year? The currentnational debt is \$17,000,000,000. Solve algebraically and show all of yourwork. Find the exact value. Assume the interest rate is 8%.