Answer:
India's population will reach 2 billion during the year of 2050.
Step-by-step explanation:
India's population in t years after 2008 is modeled by the following equation:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the population in 2008 and r is the growth rate, as a decimal.
Population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year.
This means that [tex]P(0) = 1.14, r = 0.0134[/tex]. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 1.14(1+0.0134)^{t}[/tex]
[tex]P(t) = 1.14(1.0134)^{t}[/tex]
If the population continues following this trend, during what year will the population reach 2 billion?
t years after 2008.
t is found when P(t) = 2. So
[tex]P(t) = 1.14(1.0134)^{t}[/tex]
[tex]2 = 1.14(1.0134)^{t}[/tex]
[tex](1.0134)^{t} = \frac{2}{1.14}[/tex]
[tex]\log{(1.0134)^{t}} = \log{\frac{2}{1.14}}[/tex]
[tex]t\log{1.0134} = \log{\frac{2}{1.14}}[/tex]
[tex]t = \frac{\log{\frac{2}{1.14}}}{\log{1.0134}}[/tex]
[tex]t = 42.23[/tex]
2008 + 42 = 2050
India's population will reach 2 billion during the year of 2050.
