What was India's annual exponential growth rate as per the 2011 Census?

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Accepted Answer

Step 1: The 2011 Census reported a decadal growth of 17.64%, i.e. a factor of $1.1764$ over 10 years.

Step 2: For annual exponential growth rate $r$ we solve $(1+r)^{10}=1.1764$, so

$\displaystyle r=1.1764^{1/10}-1$.

Step 3: Compute using logarithms: $\ln(1.1764)\approx0.16228$, then $r=\exp(0.16228/10)-1\approx\exp(0.016228)-1\approx0.01636\approx1.64\%$.

Thus the annual exponential growth rate is approximately $1.64\%$, option (2).

FINAL_ANSWER: b

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