Question

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?

Answer 1

The answer will depend upon what model of growth you assume will occur.
There is insufficient information to answer this question.

Explanation:

Here are a couple models (neither is likely to be accurate).

In both cases I have used the variable `y` to indicate the number of years after 2006

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Linear Model
The population (in billions) is given by the formula:
`color(white)("XXX")p=6.5+k * y` for some constant growth factor `k`

We have for the year 2013 i.e. `y=7`
`color(white)("XXX")7.1=6.5+k * 7`

`color(white)("XXX")k=0.6/7`

If this model holds, then for the year 2050 i.e. `y=44`
`color(white)("XXX")p=6.5+0.6/7 * 44 ~~ 10.27` (billion)

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Compound Model
The population (in billions) is given by an equation similar to that for the balance of an investment with a compound interest rate, `r`:
#color(white)("XXX")p=6.5(1+r)^y

We have for the year 2013 (`y=7`)
`color(white)("XXX")7.1 = 6.5(1+r)^7`

`color(white)("XXX")r=root(7)(7.1/6.5)-1`

If this model holds then for the year 2050 (`y=44`)
`color(white)("XXX")p=6.5 xx(root(7)(7.1/6.5))^44 ~~11.32` (billion)

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A more realistic model might look like:
...but the given data provides no information where along this curve the years 2006 and 2013 occur.