Question

part 2 of 4(b) use the models from parts (a) and (b) to predict the population 20 years after the initial census was taken for each country. round to three decimal places.the predicted population of the asian country 20 years after the initial census would be approximately million.the predicted population of the south pacific country 20 years after the initial census would be approximately million.

Explanation:

Step1: Find the population of South - Pacific country

We use the formula \(P(t)=20e^{0.01655t}\). When \(t = 20\), substitute \(t\) into the formula:

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Since \(e^{0.331}\approx1.392\) (using a calculator, \(e^x\) can be calculated as \(e^x=\sum_{n = 0}^{\infty}\frac{x^n}{n!}\), and for a quick calculation, we use the calculator value of \(e^{0.331}\)), then \(P(20)=20\times1.392 = 27.84\)

Step2: Find the population of Asian country

We use the formula \(P(t)=23.9e^{0.00329t}\). When \(t = 20\), substitute \(t\) into the formula:

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$$

Since \(e^{0.0658}\approx1.068\) (using a calculator), then \(P(20)=23.9\times1.068=25.525\)

Answer:

The predicted population of the South - Pacific country 20 years after the initial census is approximately \(27.8\) million. The predicted population of the Asian country 20 years after the initial census is approximately \(25.5\) million.