HardBiologyHigh School (11–12)Human BodyNumerical

NCERT says that the population of India was about 350 million at independence in 1947, and that it…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

NCERT says that the population of India was about $350$ million at independence in 1947, and that it crossed $1.2$ billion, that is $1200$ million, in 2011. Treat the growth between the two years as a steady growth by the same share every year.

How many times larger was the population in 2011 than in 1947?

What was the yearly growth rate, in per cent?

At that rate, how long does the population take to double?

Is the rate above or below $2$ per cent a year?

Need a reminder? The key ideaShow

A population that grows by $r$ per cent a year is multiplied by $1 + \dfrac{r}{100}$ every year. After $t$ years: $P = P_0\left(1 + \dfrac{r}{100}\right)^t$ . The doubling time is $\dfrac{\ln 2}{\ln(1 + r/100)}$ , close to $\dfrac{70}{r}$ years. The growth in a year, per $1000$ people, is the birth rate minus the death rate.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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