 Exponential growth describes something that grows very fast. We're going to look at doubling. Math students need be able to recognize the first ten or so powers of 2 from memory. To help, we've listed them on a separate page here that you can print. You might also want to review powers and exponents. 
Let's do a 'thought experiment'. Albert Einstein used to do them all the time: imagining something that could happen, but that you can't actually do.For example, imagine placing a single penny on the first square of a checkerboard. On the second square, you're going to place two pennies. Next, four pennies will go on the third square, and eight pennies on the fourth square. On each square after that, you will continue to place pennies, doubling every time. For example, the fifth square will get sixteen pennies, the sixth will get 32 pennies, and the seventh 64 pennies. The final square on the first row will get 128 pennies, or $1.28. It's clear why this has to be a 'thought experiment'. There's no way to get 128 pennies onto one square, even if you stack them ... and we're nowhere near done yet! Given that there are 64 squares on a checkerboard, here is a question: "How much money will be on the 64th square?" Find out the surprising answer on page two > > > |