Question

# Suppose that the current (first) generation consists of 1 million people, half of whom are women. If the total fertility rate is 1.3 and the only way people die is of old age, how big will the fourth generation (the great-grandchildren) be? How much smaller (in percentage terms) is each generation than the previous generation? How much smaller (in percentage terms) is the fourth generation than the first generation? Are you surprised by how quickly the population declines?

Solutions

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To calculate how big will the fourth generation be if the total fertility rate is $1.3$ and there are $1$ million people in the first generation, we need to figure out what will be the multiplier for each generation.

Since half of the listed $1$ million people are women, and women are those giving birth, we need to multiply the total fertility rate of $1.3$ by 50 which will give us a multiplier for each generation:

\begin{align*} 1.3 \times 50&=65\\ \end{align*}

Since $1.3$ is a rate, the calculated number is a percentage.

This also means that each generation is $35\%$ smaller than the previous generation $(1-0.65=0.35)$.