Growth (cont.)

NRR and growth

If the NRR is the average number of daughters to a woman, it can be interpreted as the ratio of one generation to another. If the length of the generation is G, then we can express this as:

NRR = PG / P0

If the initial population size is P0 and time is t, the exponential growth formula tells us that:

Pt = P0 . e rt

It follows that:

Pt / P0 = e rt

If we substitute generation length G for time = t, it follows that:

NRR = e rG

This means that we can express the NRR in terms of exponential population growth. If we knew the value for G (average generation length), we could solve the equation for r and find the annual growth rate using the following steps:

ln NRR = rG

r = ln NRR / G

Interaction Exercise: If we know the NRR, what further measure do we need to use the NRR to estimate annual growth?

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In order to calculate an annual growth rate based on the NRR, we need to know the length of a generation (G): on average, by what age do women replace themselves with their NRR daughters?