Suppose that the current (first) generation consists of 2 million people, half o

Question

Suppose that the current (first) generation consists of 2 million people, half of whom are women. Assume the total fertility rate is 1.2 and the only way people die is of old age. Instructions: In parts a and b, enter your answers as whole numbers. In part c, round your answer to 2 decimal places.

a. How big will the fourth generation (the great-grandchildren) be?

b. How much smaller (in percentage terms) is each generation than the previous generation? percent.

c. How much smaller (in percentage terms) is the fourth generation than the first generation?

Explanation / Answer

Fertility rate = 1.2 Population growth rate =1.2/2 - 1 = -0.4

a) Second generation = 2000000*(1+-0.4) = 2000000*0.6 = 1200000

Third generation = 1200000*0.6 = 720000

Fourth generation = 432000

b) Each generation is 40% smaller than previous

c) (432000-2000000)/2000000*100 = -78.4% so fourth generation is 78.4% smaller than first.

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