KathieRafala253
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A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential growth. ...?

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: $ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083$ 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