Picturing exponential growth, powers of 10, can be hard for any of us to imagine. The spreadsheet has the flexibility to enable us to explore the powers of 10 and to get a visual image of them. We can see the difference in shape between odd and even powers, and get a sense of the speed of exponential growth. We use powers of ten to gain a sense not only of big numbers but of how big spreadsheets can be.
It was one of the most amazing visions of the future ever made. In 1965 Gordon Moore, one of the founders of Intel, proposed a law governing the future of computing. He originally proposed that the number of components on a chip would double every year. Later he revised that law to doubling every two years. You can take a look at the real data of CPU development over the past 40 years and see if it in fact has followed Moore’s law and whether it can continue. In the process you will be looking at very large numbers and the effects of exponential growth on something we now live with all the time.
1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and they form a very interesting pattern when graphed.
Can you guess the next triangular number? Can you guess the shape of the graph of the triangular numbers? Can you explain that graph?
The rule of 72 is an old banker’s rule of thumb to find out how long it will take to double your money at different interest rates. Financial literacy has become an increasingly important topic for K-12 education and we believe spreadsheets and headmath or mental estimation should be central to it. Rule of 72 combines both and gets students calculating compound interest. They can also see how expensive high credit card interest rates can be to them.
We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2 grow in size. We start out with a chessboard and look at doubling each successive number. Then we seek a method of representing this doubling in a formula and introduce exponents and powers of 2. We ask you what kind of rule would you suggest that would keep your head and please the ruler?