# In 2012, the worlds population was 7 billion and the population was projected to reach 8 billion by the year 2025. What was the annual growth rate projected? Round to four decimals.

In 2012, the worlds population was 7 billion and the population was projected to reach 8 billion by the year 2025. What was the annual growth rate projected? Round to four decimals.
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Pohanginah
Since the population growth equation is given by:
$P={P}_{0}{e}^{rt}$
${P}_{0}$ is the initial population in billions at time t, t is the number of years since 2012, r is the rate of growth of population per year.
So In this case,
${P}_{0}=7bn$

$P=8bn$
Hence substituting these values in the population growth equation,
$8=7{e}^{13r}$

$\mathrm{ln}\left({e}^{13r}\right)=\mathrm{ln}\left(\frac{8}{7}\right)$
$13r=\mathrm{ln}\left(\frac{8}{7}\right)$

Answer: The annual growth rate of population is given below,
per year.