Rethinking the Curriculum: Toward an Integrated, Interdisciplinary College Education

By Mary E. Clark ; Sandra A. Wawrytko | Go to book overview

14 FORGOTTEN FUNDAMENTALS OF STEADY GROWTH

Albert A. Bartlett


INTRODUCING THE EXPONENTIAL FUNCTION

As a scientist, I happen to believe that the greatest shortcoming of the human race is our inability to understand the exponential function. The "exponential function" is the mathematical statement we write down to describe the size of anything that is growing steadily. If something is growing at 5 percent per year, the exponential function would show how large that growing quantity becomes, year after year. We are talking about a situation where the time required for the quantity to increase by a fixed fraction is a constant. So for 5 percent per year, the 5 percent is a fixed fraction and the year is a fixed length of time. That is what we want to talk about: ordinary, steady growth.

If it takes a fixed length of time to grow by 5 percent, it follows that it takes a longer fixed length of time to grow by 100 percent (to double). This longer time is called the doubling time, T2, and it is easy to calculate. You just take the number 70, divide it by the percent growth per unit time, P, and that gives you the doubling time.

For our example of 5 percent growth per year, we divide 5 into 70 and find that the growing quantity will double in size every 14 years. (The number 70 is roughly 100 times the natural logarithm of two, but just remember 70.)

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