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In a country, the number of births in a year for every 1000 people (the birth rate) and the number…

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

In a country, the number of births in a year for every $1000$ people (the birth rate) and the number of deaths for every $1000$ people (the death rate) were measured twice. In 1950, the birth rate was $30$ and the death rate was $20$ . In 2000, the birth rate was $25$ and the death rate was $8$ .

What was the yearly growth rate in 1950, in per cent?

What was it in 2000, in per cent?

The birth rate fell. Why did the growth rate still rise?

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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