Question

Question was provided via image upload.

Explanation:

Identify given values and formulas

Using the Approximate Half-Life Formula and Approximate Growth Factor knowledge points

• Initial population in 2020: \(P_0 = 330\text{ million}\)
• Annual growth rate: \(r = 0.9\% = 0.009\)
• Approximate doubling time formula: \(T_{\text{double}} \approx \frac{70}{r \times 100} = \frac{70}{0.9} \approx 77.78\text{ years}\)
• Population model: \(P(t) = P_0 \times 2^{t / T_{\text{double}}}\)

Calculate predicted population in 2050

Using the Population Trend Prediction knowledge point

• Time elapsed from 2020 to 2050: \(t = 2050 - 2020 = 30\text{ years}\)
• Population calculation:

$$ P(30) = 330 \times 2^{30 / 77.78} \approx 330 \times 2^{0.3857} \approx 330 \times 1.3065 \approx 431.1\text{ million} $$

• Rounded to the nearest whole number: \(431\text{ million}\)

Calculate predicted population in 2110

Using the Population Trend Prediction knowledge point

• Time elapsed from 2020 to 2110: \(t = 2110 - 2020 = 90\text{ years}\)
• Population calculation:

$$ P(90) = 330 \times 2^{90 / 77.78} \approx 330 \times 2^{1.1571} \approx 330 \times 2.2301 \approx 735.9\text{ million} $$

• Rounded to the nearest whole number: \(736\text{ million}\)

Answer:

Question 1

What is the predicted population in 2050?
<blank>431</blank> million

Question 2

What is the predicted population in 2110?
<blank>736</blank> million