Question

If the world's population increased exponentially from 5.937 billion in 1998 to 6.771 billion in 2008 and continued to increase at the same percentage rate between 2008 and 2012, calculate what the world's population would have been in 2012. how does this compare to the population reference bureau estimate of 7.07 billion in july 2012?

Answer 1

Answer:

The world's population would have been 7.1137 billion in 2012, and this is 0.0437 billion (i.e. 7.1137 - 7.07 = 0.0437) higher compared to the population reference bureau estimate of 7.07 billion in July 2012.

Explanation:

This can be computed using the following exponential formula:

P(t) = P(0)a^t ............................ (1)

Where;

P(t) = World population in year t.

P(0) = World population in year 0 which is 1998 = 5.937 billion

a = base = ?

t = number of years

Substituting the value into equation (1), we have:

P(t) = 5.937 * a^t .......................................... (2)

Since we have 10 years from 1998 to 2008 (i.e. 2008 - 1998 = 10), we have:

P(t) = P(10) = World population in 2008 = 6.771 billion

t = 10

Substituting the value into equation (2) and solve for a, we have:

6.771 = 5.937 * a^10

a^10 = 6.771 / 5.937

a^10 = 1.1405

a = $\sqrt[10]{1.405}$

a = 1.013

Since we have 14 years from 1998 to 2012 (i.e. 2012 - 1998 = 14), we now have:

P(t) = P(14) = World population in 2012 = ?

P(0) = World population in year 0 which is 1998 = 5.937 billion

a = 1.013 as already calculated above

t = 14

Substituting the value into equation (1), we have:

P(14) = 5.937 * 1.013^14

P(14) = 5.937 * 1.192

P(14) = 7.1137 billion

Therefore, the world's population would have been 7.1137 billion in 2012, and this is 0.0437 billion (i.e. 7.1137 - 7.07 = 0.0437) higher compared to the population reference bureau estimate of 7.07 billion in july 2012.