Greenwood press

30
EXPONENTIAL GROWTH

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and ruined grazing areas for sheep. During the thirty years after their introduc-
tion, the rabbit population doubled every six months. The table and graph below
show the approximate number of rabbits in Australia for each six-month period
after the introduction of Mr. Austin’s original 24 rabbits.
The equation for the number of rabbits is 
y = 24 • 2
x
. Because the inde-
pendent variable 
x is in an exponent, the equation describing the rabbit popula-
tion growth is called an exponential model. The base 2, which represents dou-
bling, is the growth factor. Growth factors greater than one create curves similar
to the rabbit-population curve. When the growth factor is less than one, the curve
will decrease (see Exponential Decay).
Exponential growth models are used extensively in the world of finance.
Investments of money in a certificate of deposit (CD), for example, require the
customer to invest a certain amount of money (principal) for a specified time.
The bank issuing the CD will specify an annual yield, a yearly interest rate that
will be added to the principal each year. The interest becomes part of the princi-