Mathematics
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. ...?

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(1) Answers
ItssHannahh

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

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