### What is an example of real life exponential function?

That depends whether we're talking about a general definition of an exponential function or a technical definition (using an exponent of Euler's constant).In the former case, there are lots of examples: working out radio-active half-life or the operation of compound interest, to name a couple.In the latter case, I think it's used for theoretical simulations of mind-bending complexity, such as how a machine might rattle itself to bits... when you want to know the maximum impact of multiple worsening faults on each other (I think).Ok, I'll have a go. Construct a rather large cage; put in a male rabbit and a female rabbit. Arrange for a good supply of food and water. Count the population every month and plot it on a graph. It would really help you to understand what is going on if you removed any dead rabbits at once, but allowed for them when trying to analyse your numbers. If you are impatient, you could get the same results much faster using fruit flies, but they are oh so hard to count. -Another- Bacterial growth is a classic exponential growth Say you begin with one bacterium and it takes 24 hours to divide... At t=0 days there would be just the one bacterium. At t=1day, there would be two, which would divide and at t=2, there would be four etc. A graph of population size against time could be plotted... you would find that population size = 2^time. This is exponential.