Now let's move from thinking about bank accounts to thinking about nature.
Consider the earth's human population, which is increasing exponentially. If
we are given an annual growth rate and want to predict the earth's population
in ten years, what compounding interval should we use? After all, new babies
are not credited to the earth's account only at the end of every year, every
month, or every day. They arrive more or less continuously.
When exponential growth occurs in nature, we use what amounts to
continuous compounding. Continuous compounding is what we get when we let the
number of compounding intervals approach infinity. That is, we receive an
infinite number of extremely tiny interest payments.
Beginning with the formula for computing exponential growth for different
compounding intervals, can you think of a way of coming up with a function
called continuous that computes the results of exponential growth under
continuous compounding?
Click here for the answer
When you are doing calculations involving exponential growths in nature, you
should use the formula for continuous compounding. You should try it out. The
population of the United States is currently around 260 million. If the
population increases at an annual rate of 1%, what will be the population of
the United States in 100 years?
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah