Life Expectancy Calculation from Birth Rate

The relationship between the life table birth rate and life expectancy at birth can be understood using principles of population dynamics. In a stable or stationary population, the birth rate and death rate are constant and balanced over time.

A common interpretation in population studies is that the crude birth rate (CBR) is often expressed per 1000 individuals. If the "life table birth rate" given is 10, we can assume this represents 10 births per 1000 individuals.

Step 1: Convert Birth Rate to Per Capita Rate

Convert the given rate (10 per 1000) into a per capita birth rate ($b$):
$b = \frac{10}{1000} = 0.01$

Step 2: Relate Birth Rate to Life Expectancy

For a population that is stable (meaning the number of births balances the number of deaths and the age structure remains constant), the life expectancy at birth ($e_0$) is approximately the inverse of the per capita birth rate (or death rate, as they are equal in a stable population).
$e_0 \approx \frac{1}{b}$

Step 3: Calculate Life Expectancy

Substitute the per capita birth rate into the formula:
$e_0 \approx \frac{1}{0.01} = 100$

Therefore, the life expectancy at birth is approximately 100 years.