Question

India is the second most populous country in the world, with a population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year. If the population continues following this trend, during what year will the population reach 2 billion?

Answer 1

India's population will reach 2 billion during the year of 2050.

Explanation:

India's population in t years after 2008 is modeled by the following equation:

`P(t) = P(0)(1+r)^(t)`

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
`P(0) = 1.14, r = 0.0134`. So

`P(t) = P(0)(1+r)^(t)`

`P(t) = 1.14(1+0.0134)^(t)`

`P(t) = 1.14(1.0134)^(t)`

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

`P(t) = 1.14(1.0134)^(t)`

`2 = 1.14(1.0134)^(t)`

`(1.0134)^(t) = (2)/(1.14)`

`\log{(1.0134)^(t)} = \log{(2)/(1.14)}`

`t\log{1.0134} = \log{(2)/(1.14)}`

`t = \frac{\log{(2)/(1.14)}}{\log{1.0134}}`

`t = 42.23`

2008 + 42 = 2050

India's population will reach 2 billion during the year of 2050.