Question

The population of a town is 20,000. If the annual birth rate is 4% and the annual death rate is 2%. Calculate the population after two years.

Answer 1

Hint: We will first calculate the net percentage change in a year when annual birth rate is 4% and annual death rate is 2%. Next, calculate the population increase in one year and find the population after one year. Then, find the population increase after the first year and add it to the population of the first year to find the population after the second year.

Complete step-by-step answer:
We are given that the annual birth rate is 4% and the annual death is 2%.
First of all we will calculate the net change in rate in population by finding the difference in birth rate and death rate.
Hence, the net rate is $4\% - 2\% = 2\% $
There will be an increase in population by 2%
We will now calculate the increase in population
That is, we will find 2% of 20,000
$\dfrac{2}{{100}} \times 20,000$
On simplifying the expression, we get,
$\dfrac{2}{{100}} \times 20,000 = 400$
Then, population after one year is $20,000 + 400 = 20,400$
But, we have to calculate the population after 2 years.
Now, we will find the number of people increased in the second year.
Hence, we will find 20% of 20,400
That is, $\dfrac{2}{{100}} \times 20,400 = 408$
Now the population after 2 years is $20,400 + 408 = 20,808$
Therefore, the population of the village after two years is 20,808.

Note: Here, we have calculated the net change in population by taking the difference of annual birth rate and annual death rate. If the net change is positive, then there is an increase in population. If the net change is negative, it means there is a decrease in population.