Have you ever heard the expression “growing exponentially”? This phrase is often misused, but in fact some things do change exponentially, for instance, the population of a large city, …
… a tiny village, …
… or even bacteria in a Petri dish.
When used correctly, “exponential growth” has a very specific meaning. An exponential function is a function that has a fixed number, a constant called the base, raised to a variable power.
More specifically, an exponential function could also have a constant coefficient, and another coefficient for the variable power.
Mathematical entities that have exponential parts can come in many forms, but exponential functions are defined as shown here: f of x is equal to I times b to the k x power. Here l, b and k are all constant values. x is the only variable.
This simulation will allow you to experiment with exponential functions. There are three sliders supplied, one for each of the three constants.
You could also type values into the fields above the sliders. I and b are restricted to positive values, and b cannot be equal to one. k can take any non-zero value, positive or negative.
There is a special value for the base of exponential functions that is often preferred by engineers, scientists, and mathematicians. It is denoted by the letter e, and its value is approximately 2.718281828459.
You can enter this value for the base by clicking on the button supplied at the bottom of the interface.
Use different combinations of values for the three parameters. Try positive and negative values for k, and small values as well as large for b.
Look for trends and patterns. There are many things to learn about exponential functions beyond this simulation. Use this opportunity to get a good introduction to them, Good luck!