exponential function

Comparison with exponential function f(x)=2^x
  • “The greatest shortcoming of the human race is our inability to understand the exponential function.” –Al Bartlett

Arithmetic, Population and Energy (video 10:55) – a talk by Al Bartlett. He gives a basic introduction to the arithmetic of steady growth, including an explanation of the concept of doubling time. He explains the impact of unending steady growth on the population of Boulder, of Colorado, and of the world. It is essential that everyone understand and appreciate the implications of unending growth on a finite planet.

Real world

  • Exponential functions are used in banking and finance to calculate compound interest.
  • Radioactive decay, population growth – these can be modeled using exponential functions.

What’s the problem?
Suppose that you plan to need $10,000 in thirty-six months’ time when your child starts attending university. You want to invest in an instrument yielding 3.5% interest, compounded monthly. How much should you invest?

  • Ask – Is this a compound interest problem?
  • Imagine
  • Plan, Createsolving the problem
  • Improve

Learn more…