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
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
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%.