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In 2014, the populations of China and India were approximately 1.355 and 1.255 billion people,45 respectively. However, due to central control the annual population growth rate of China was 0.44% while the population of India was growing by 1.25% each year. If these growth rates remain constant, when will the population of India exceed that of China?

Respuesta :

Answer:

in the year 2023

Step-by-step explanation:

Initial population of China = 1.355  billion

Initial population of India = 1.255  billion

Annual population growth rate of China = 0.44% = 0.0044

Annual population growth rate of India = 1.25% = 0.0125

Now,

Final population = Pâ‚€ [tex]\times e^{\text{rate}\times t}[/tex]

Here,

Pâ‚€ = initial population

t = time

Thus,

Population of India > Population of China

1.255[tex]\times e^{\text{0.0125}\times t}[/tex]  > 1.355[tex]\times e^{\text{0.0044}\times t}[/tex]  

or

[tex]e^{0.0081t}[/tex] > 1.07968

taking natural log both sides

0.0081t > ln (1.07968 )

or

0.0081t > 0.0766

or

t > 9.465

Hence,

9.465 year after 2014

i.e

in 2014 + 9.465 = 2023.46

in the year 2023

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