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: [tex]120 000 000 = 114 000 000 * e ^{n*6} \\ e ^{n*6} =120 000 000 /114000000 \\ e ^{n*6} =1.05 \\ [/tex] Logarithm both sides of the equation: [tex]ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083[/tex]
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 [tex]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
[/tex] Thus, the population will be 138 million in 2014
