# In 1950 the world population was 2.5 billion. The population doubled to 5 billion in 1987.What was the annual growth rate of the world population from 1950 to 1987?

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For an exponential growth, we can have the population modelled by the function

`A=A_0(1+r)^t` where `A_0` is the initial population, `r` is the growth rate, `t` is the time difference and `A` is the final population.

Now we just substitute all the numbers for the model, then solve for `r` to get the growth rate of the world population.

After substitution we get

`5=2.5(1+r)^{1987-1950}` divide both sides by 2.5 and subtract years

`2=(1+r)^37` take 37th root

`2^{1/37}=1+r` solve for r

`2^{1/37}-1=r`

`r approx 0.0189 = 1.89%`

**The annual growth rate of the population was 1.89%.**