Math in the News: 8/8/11

8/8/11

Federal $pending

This table shows the total government expenditures from 2000 to 2010. During this ten-year period, expenses doubled in size.

Source: http://www.whitehouse.gov/omb/budget/Historicals

Federal $pending

Here is a graph of the data from the table.

Federal $pendingThe change

from 2000 to 2010 represents a 93% increase.

Federal $pendingHow can we

use this result to determine the average year-to-year increase?

Federal $pendingUse this

formula, which shows an annual increase in spending of a constant Rate.

Federal $pending

We need to solve for the Rate.

Federal $pendingThe result is

that each year, on average, the federal budget grew by a little over 6%.

Federal $pending

• Are you surprised by the result?• Were you expecting that the annual percent increase in the budget would

be much larger than 6.8%

Federal $pendingThis is an

example of the power of compound growth.

Federal $pendingA simple way of

estimating how long it takes to double an amount of money, assuming simple interest compounded annually, is to use the Rule of 72.

Federal $pendingA graph of the

Rule of 72 results in a rational function. The y- coordinate is the number of years it takes, given the compounding rate in the x- coordinate.

US. Govt. spending: Doubles every dozen years.

Federal $pending

Next Steps

• Write a letter to your Senator or Congressman about the topic of federal spending. List some of your recommendations for controlling the growth of federal spending over the next ten years.

• BASE ALL OF YOUR RECOMMENDATIONS ON DATA THAT YOU HAVE OBTAINED AND ANALYZED.