# The equation y=6.72(1.014)^x models the world population y, in billions of people, x-years after the year 2000. Find the year in which the world population is about 10 billion?

##### 1 Answer
Jun 3, 2015

$y = 6.72 \cdot {\left(1.014\right)}^{x}$

$10 = 6.72 \cdot {\left(1.014\right)}^{x}$

$\frac{10}{6.72} = {1.014}^{x}$

$\log \left(\frac{10}{6.72}\right) = \log \left({1.014}^{x}\right)$

$\log \left(\frac{10}{6.72}\right) = x \cdot \log \left(1.014\right)$

$x = \log \frac{\frac{10}{6.72}}{\log} \left(1.014\right) = \frac{\log \left(10\right) - \log \left(6.72\right)}{\log} \left(1.014\right)$

$x = \frac{\log \left(10\right) - \log \left(6.72\right)}{\log} \left(1.014\right) = \frac{1 - \log \left(6.72\right)}{\log} \left(1.014\right) \approx 28.59 .$

So the world population would reach 10 billion in the middle of year $2028$. In fact it is expected to be around 2100.

https://en.wikipedia.org/wiki/World_population