I gave an example in College Algebra yesterday about the U.S. GDP and Chinese GDP. We were talking about exponential functions, and I made up some numbers and asked the students to find when the Chinese GDP would be larger than the U.S. GDP. The year we got with my numbers was 2049. After I finished the example, I told the students about Hans Rosling's talk on TED about when Asian per capita income would be larger then the U.S. per capita income. He came up with the year 2048.
I was amazed how close our dates were, even though he is using real data and I just made up numbers. So, I showed the class WolframAlpha and we were able to find graphs of the Chinese GDP and U.S. GDP over the past sixty years. Both graphs generated by WolframAlpha looked appropriately exponential.
I was wrong about the starting values for the economies in 2000 (I guessed 4 trillion dollars for the US and 400 billion dollars for China) but the ratio between my guesses and the actual values was correct (10 trillion for the US and 1 trillion for China). I was confident in my estimates for the growth rate for both economies (4% for the U.S. and 9% for China) because I got them off of the news over the past few years.
In my last post, I discussed overuse of programs like WolframAlpha in teaching. I felt like a hypocrite when I used WolframAlpha in class. In my defense, I never did say it was a bad program, just that it shouldn't be the foundation for a mathematics curriculum. For the record, we did solve the equation that we developed in class by using graphing calculators.