The document discusses federal spending from 2000 to 2010. It shows that total government expenditures doubled during this ten-year period, representing a 93% increase. By analyzing the data, the document determines that on average, the federal budget grew by slightly over 6% each year over this time period. This example demonstrates the power of compound growth and how spending can double relatively quickly at an annual growth rate below 10%.

1. 8/8/11

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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

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Here is a
graph of the
data from
the table.

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The change
from 2000 to
2010
represents a
93% increase.

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How can we
use this result
to determine
the average
year-to-year
increase?

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

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We need to
solve for the
Rate.

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

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• Are you surprised by the result?
• Were you expecting that the annual
percent increase in the budget would be
much larger than 6.8%

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This is an
example of the
power of
compound
growth.

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A 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.

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A 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.

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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.