Question

A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential growth. ...?

Answer 1

The answer is 138 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:

`120 000 000 = 114 000 000 * e ^(n*6) \\ e ^(n*6) =120 000 000 /114000000 \\ e ^(n*6) =1.05 \\`
Logarithm both sides of the equation:

`ln(e ^(n*6))=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = (ln(1.05))/(6) \\ n = (0.05)/(6) \\ n = 0.0083`

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17

`A = 120 000 000 * e ^(0.0083*17) \\ A = 120 000 000 * e^(0.1411) \\ A = 120 000 000 * 1.15 \\ A = 138 000 000`
Thus, the population will be 138 million in 2014