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

Correct — A. The 2011 Census puts India's average annual exponential growth rate at 1.64% for the decade 2001-2011, down from 1.97% for 1991-2001.

You can check it against the decadal figure you already know. A rate r compounding continuously over ten years multiplies the population by e raised to 10r:

e^(10 x 0.0164) = e^0.164 = 1.178, about 17.8% growth over the decade.

The Census recorded decadal growth of 17.7%, so 1.64% is the annual rate that reproduces it.

Why the others are wrong

• (b)
  3.54% — Run the same check: e^0.354 = 1.42, a 42% rise in ten years. No Indian census decade has recorded growth anywhere near that.
• (c)
  1.10% — The near-miss. e^0.11 = 1.116, which is about 11.6% decadal growth — well short of the 17.7% the 2011 Census actually recorded.
• (d)
  4.34% — e^0.434 = 1.54, a 54% decadal rise. That would have added more than half of India's population in a single decade.

The Census reports growth in two ways, and the two must agree.

The decadal growth rate is the plain percentage increase between two censuses: 17.7% for 2001-2011.

The average annual exponential growth rate is the smooth annual rate that would produce it, defined by the relation P2 = P1 x e^(rt). For 2001-2011 that rate is 1.64%.

The figure matters because it is falling — 1.97% for 1991-2001 against 1.64% for 2001-2011. India's population is still growing, but more slowly with each decade.

Key facts

• The 2011 Census recorded an average annual exponential growth rate of 1.64%.
• Decadal population growth for 2001-2011 was about 17.7%.
• The exponential growth rate for 1991-2001 was 1.97%.
• India's population at the 2011 Census was about 121 crore.

Common traps

• Giving the decadal growth rate of 17.7% when the stem asks for the annual rate.
• Treating the exponential rate as a simple annual percentage, which would give 16.4% over ten years instead of about 17.8%.

No directly related past PYQ was found.