Sometimes I wish I was a student again...

... taking Brad de Long's exam:

No calculators allowed, You won’t need them. All you will need is simple arithmetic (the ability to multiply things by two, and to divide) and the rule of 72—the fact that a quantity growing at 1% per year doubles in 72 years, a quantity growing at 2% per year doubles in 36 years, a quantity growing at 0.5% per year doubles in 144 years, et cetera, a quantity growing at 1% per year grows by 41.41% in 36 years, etc…

PART 3 (25 MINUTES): Calculations

Consider the 144 years between 1866 and 2010…

1. World population grew from about 1.1 billion to 6.4 billion. About how many doublings did population undergo? What is the average growth rate of world population over those 144 years?
2. World total real GDP (on one somewhat arbitrary set of assumptions, at least) grew from $875 billion of today’s dollars in 1866 to $56 trillion of today’s dollars today. What was the average growth rate of world total real GDP over those 144 years?
3. If world total real GDP growth continues to grow at its average 1866-2010 rate, what will world total real GDP (in today’s dollars) be in 2155? Do you think this is possible? Reasonable? Absurd? Why?
4. By contrast, total world GDP (on one somewhat arbitrary set of assumptions, at least) grew from $437.5 billion of today’s dollars in 1794 to $875 billion of today’s dollars in 1866. Suppose total world real GDP growth had continued at its 1794-1866 pace from 1866-2010. What would total world real GDP be today?

If I follow correctly. 2. implies 6 doublings in 144 years or an annual growth rate of 3%.
4. implies a growth rate of 1% (1 doubling in 72 years) continuing at that pace for an other 144 years the economy would have experienced two doublings to 3.5 trillion, not even 10% of today's size. Amazing!