Self Check Answers

1. The compound interest formula is not just for banking but for any "population" that increases geometrically (exponentially).
2. The data point for 1940 reflects a low birthrate during the Great Depression in the 1930s.
3. We could import it, a rising price would reduce use, or we would find substitutes.
4. 28.5 years
5. Reducing to takes about 10 half-lives, since . Since , reducing to takes not quite 7 half-lives, hence a little less than days.

   978

7. The age would then be about 16,500 years.
8. The populations over the next years are 10 (this year), minus harvest of 6, leaving 4; 7.5, minus harvest of 6, leaving 1.5; 5, minus harvest of 6, resulting in extinction.
9. Just go to a subway stop and wait for a train that (via connections) goes to where you want to go.
10. After 02, you wind up eventually in the same loop as when starting with 37 or 38: 04, 08, 16, 32, 64, 28, 56, 12, 24, 48, 96, 92, 84, 68, 36, 72, 44, 88, 76, 52, 04, …. It can be shown that the length of the loop (20) must divide the modulus (100).
11. The sequence goes 0.5 00, 0.675, 0.5 92, 0.65 2, 0.613, 641, …, and centers down on 1.7/2.7 ≈ 0.630.