# If the population of the world was 6.5 billion in 2006 and is currently 7.1 billion (in the year 2013), what will the population be in the year 2050?

Jan 16, 2017

10.4 billions.

#### Explanation:

There are quite many models, for population growth.

The models can be compared, for relative merits.

Here, only two starter data are available. So, I choose a 2-

parameter model. applicable for any growth.

If the year Y = 0 at 2006 and P is the population after Y years,

$P = {P}_{0} {e}^{k Y}$

When, Y = 0, P was 6.5 billions. So, #P_0=6.5.

When it was 7 years from then, Y = 7 and

$7 = 6.5 {e}^{7 k}$, giving ${e}^{7 k} = \frac{7}{6.5}$

On this time scale, at 2050, Y = 44, and so, P then will be

P(Y=44)

$= 6.5 {e}^{44 k}$

$= 6.5 {\left({e}^{7 k}\right)}^{\frac{44}{7}}$

$= 6.5 {\left(\frac{7}{6.5}\right)}^{\frac{44}{7}}$

$= 10.4$ billions, rounded to 3-sd.