12.58 Future shock Refer to the previous exercise, for which predicted population growth was 14.18% per decade.

Suppose the growth rate is now 15% per decade. Explain why the population size will

(a) double after five decades,

(b) quadruple after 100 years (10 decades), and

(c) be 16 times its original size after 200 years. (The exponentially increasing function has the property that its doubling time is constant. This is a fast increase, even though the annual rate of growth seems small.)