Exponential Growth: an interesting application

Tutoring math 12, exponential growth is “always on my mind.”

Years ago, I used to read the Economist.  Eventually I became too busy to keep up with it, but I always enjoyed it when I could.

One of the last articles I remember (this was maybe in ’05 or ’06), China’s economy was being compared with India’s. ¬†At the time, China’s growth was 8%, while India’s was 6%. Either rate would signify wildfire growth in a developed economy; I’d say Canada will be lucky to grow at 2% this year. However, the article said that India’s growth, while a very nice 6%, melted in comparison with China’s 8%.

As a math tutor, I thought about that comment for a moment. “Is 8% really that much more than 6% growth?” I asked myself.

The key is that it’s exponential growth. This year’s growth becomes a part of next year’s economy, which then grows again, so you get growth on growth on growth. That’s exponential growth: anything natural grows that way. My earlier article here talks more about it.

Reading that earlier article, you’ll also encounter the law of 72, which states the following about an economic entity:

(growth rate)x(doubling time)=72.

It’s an approximation, but a very good one.

Let’s compare India’s historic growth at 6% with China’s at 8% using the law of 72. Does 8% really “melt” the 6%? Well, what we can say is that, by the law of 72, India’s economy will double every 12 years, while China’s will double every 9 years. For simplicity, let’s imagine the economies begin at the same size. In 36 years, India’s will double three times (every 12 years), so it will be 8 times its original size. (2x2x2=8). In that same period of 36 years, China’s will double four times (every 9 years), reaching 16 times original size. (2x2x2x2=16). If they were the same size at the beginning, China’s economy, having doubled an extra time, is exactly twice India’s at the end of the 36 years.
 
From that point of view, the difference in the growth rates is impressive.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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