We have the following:
The formula that corresponds to the calculation of the population is as follows
[tex]P=A\cdot(1+r)^t[/tex]
Where A is the population of 952 108 000 inhabitants, r is the growth rate and t is the time elapsed
a.
2000
[tex]\begin{gathered} t=2000-1996=4 \\ P=952,108,000\cdot(1+0.013)^4=1002591447.8\cong1,002,600,000 \end{gathered}[/tex]
2010
[tex]\begin{gathered} t=2010-1996=14 \\ P=952,108,000\cdot(1+0.013)^{14}=1140823475.4\cong1,140,800,000 \end{gathered}[/tex]
b.
In this case what we must do is replace by 10, which is the equivalent in years of a decade in the part of the equation that corresponds to growth
[tex]\begin{gathered} (1+0.013)^{10}=1.13787 \\ 1.13787-1=0.1378 \end{gathered}[/tex]
That is, the growth is approximately 13.78%
c.
In this case, we must calculate until 2000 with the percentage of 1.3% and then from 2000 until 2010 calculate with the new growth rate
A then would be the population calculated in part a, that is, 1,002,600,000 and t would be 10 (2010 - 2000)
replacing
[tex]P=1,002,600,000\cdot(1+0.01)^{10}=1107494142.9\cong1,107,500,000[/tex]
Therefore with the new growth rate the population in India in 2010 would be 1,107,500,000
