Answer :
To predict the world's population in the year 2020, given the population in 1994 and the annual growth rate, follow these steps:
1. Identify the given values:
- Initial population in 1994 ([tex]\(P_0\)[/tex]) = 5,642,000,000 people.
- Annual growth rate ([tex]\(i\)[/tex]) = 1.3% = 0.013.
- Number of years from 1994 to 2020 ([tex]\(n\)[/tex]) = 2020 - 1994 = 26 years.
2. Use the population growth formula:
[tex]\[ P_n = P_0 e^{i n} \][/tex]
- Here, [tex]\( P_n \)[/tex] is the population after [tex]\( n \)[/tex] years, [tex]\( P_0 \)[/tex] is the initial population, [tex]\( i \)[/tex] is the growth rate, and [tex]\( n \)[/tex] is the number of years.
3. Substitute the given values into the formula:
[tex]\[ P_{2020} = 5,642,000,000 \times e^{0.013 \times 26} \][/tex]
4. Calculate the exponent:
[tex]\[ 0.013 \times 26 = 0.338 \][/tex]
5. Calculate the value of [tex]\( e^{0.338} \)[/tex]:
[tex]\[ e^{0.338} \approx 1.402 \][/tex]
6. Multiply the initial population by this value:
[tex]\[ P_{2020} = 5,642,000,000 \times 1.402 \][/tex]
7. Get the predicted population for the year 2020:
[tex]\[ P_{2020} \approx 7,910,876,720.212818 \][/tex]
8. Round this result to the nearest million:
[tex]\[ P_{2020} \approx 7,911,000,000 \][/tex]
So, the predicted population of the world in the year 2020, rounded to the nearest million, is approximately 7,911,000,000 people.
Hence, the correct answer from the given choices is:
[tex]\[ \boxed{7,911,000,000} \][/tex]
1. Identify the given values:
- Initial population in 1994 ([tex]\(P_0\)[/tex]) = 5,642,000,000 people.
- Annual growth rate ([tex]\(i\)[/tex]) = 1.3% = 0.013.
- Number of years from 1994 to 2020 ([tex]\(n\)[/tex]) = 2020 - 1994 = 26 years.
2. Use the population growth formula:
[tex]\[ P_n = P_0 e^{i n} \][/tex]
- Here, [tex]\( P_n \)[/tex] is the population after [tex]\( n \)[/tex] years, [tex]\( P_0 \)[/tex] is the initial population, [tex]\( i \)[/tex] is the growth rate, and [tex]\( n \)[/tex] is the number of years.
3. Substitute the given values into the formula:
[tex]\[ P_{2020} = 5,642,000,000 \times e^{0.013 \times 26} \][/tex]
4. Calculate the exponent:
[tex]\[ 0.013 \times 26 = 0.338 \][/tex]
5. Calculate the value of [tex]\( e^{0.338} \)[/tex]:
[tex]\[ e^{0.338} \approx 1.402 \][/tex]
6. Multiply the initial population by this value:
[tex]\[ P_{2020} = 5,642,000,000 \times 1.402 \][/tex]
7. Get the predicted population for the year 2020:
[tex]\[ P_{2020} \approx 7,910,876,720.212818 \][/tex]
8. Round this result to the nearest million:
[tex]\[ P_{2020} \approx 7,911,000,000 \][/tex]
So, the predicted population of the world in the year 2020, rounded to the nearest million, is approximately 7,911,000,000 people.
Hence, the correct answer from the given choices is:
[tex]\[ \boxed{7,911,000,000} \][/tex]
