Greenwood press

32
EXPONENTIAL GROWTH

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cannot continue exponential growth, and other models become more appropriate.
(See Logistic Functions.)
The federal government keeps close tab on exponential growth situations that
can or may harm the U.S. economy. Inflation is the growth in prices over time.
One measure of inflation is the Consumer Price Index (CPI), which provides
averages of what standard goods and services would cost each year. In the United
States, what cost $100 in 1980 would cost $228.69 in 2000. The value of a dol-
lar was therefore less in 2000 than it was in 1980. This corresponds to a yearly
increase in costs of about 4.2 percent. This can be checked with the exponential
growth calculation 
100(1 + 0.042)
20
≈ $227.70. This inflation is not a serious
national problem if wages and salaries increase at the same rate. It becomes a cri-
sis if the costs of goods and services increase at too high a percentage. There was
a time during the last twenty years in which the inflation rate in Brazil reached
80 percent per month! Using the exponential growth equation, that means that
what cost $100 at the start of the year would cost 
100(1 + 0.80)
12
≈ $1,157 at
the end of the year. 
Exponential growth is an issue in studies of the environment. From 1950
through 1970, it appeared that world oil production was increasing exponentially
at a rate of 7 percent per year to meet the growing worldwide demand. Could that
continue? Because it is harder to find previously undiscovered oil deposits, oil
production has not increased exponentially since 1970. Some scientists contend
that the carbon dioxide content in the upper atmosphere is increasing exponen-
tially. There are few dangerous effects in the early stages of the growth, but as
the amount of atmospheric CO
2
leaps ahead, serious changes such as global
warming will disrupt life on earth.
Exponential growth models are the basis of many scams, such as the chain
letter. A chain letter offers the promise of easy money. One letter might have five
names at the end of it. “Send $10 to the first name on the list. Remove that name
and put your name on the bottom of the list. Send copies of the new letter to five
people.” If you and everyone else does this, the person at the top of the list would
receive $6,250. However, by the time your name came up on top of the list,
1,953,125 people would have had to pass on the chain letter after it had been ini-
tiated. In three more stages, the letter would have to be continued by more peo-
ple than there are in the United States. Because the number of contributors to the
letter must grow exponentially, the only people who benefit from a chain letter
are those who start them. The U.S. Postal Code prohibits chain letters. However,
variants of chain letters that don’t ask for money have been popular via email.
Because these letters ask the recipient to send copies of the letter to all people in
their computer address books, the number of these messages increases very rap-
idly and can clog disk storage and communication links.
There are several other ways in which exponential growth appears in finan-
cial deceits. An entrepreneur will advertise franchises for selling some product.
For payment of a franchise fee, such as $1,000 or $5,000, the franchisee obtains
the rights to sell the product in a certain area. Up to that point, everything is legal.
But some frauds depend on the franchisees selling further franchises, with every-