The population of a city increases every year at the rate of 5%. If the population of the city is 16000, what will be the population after 2 years?

The correct answer is 17640.

When a population grows at a fixed percentage each year, it follows compound growth. This means each year's increase is calculated on the new (already-grown) population, not just the original figure.

The formula for compound population growth is:

P=P_0\times {(1+\frac{r}{100})}^n

Where:
P_0 = Initial population = 16000
r = Rate of increase per year = 5%
n = Number of years = 2

Step 1: Substitute the known values into the formula.

P=16000\times {(1+\frac{5}{100})}^2

Step 2: Simplify the bracket.

1+\frac{5}{100}=1+0.05=1.05

Step 3: Square the bracket value.

{1.05}^2=1.05\times 1.05=1.1025

Step 4: Multiply by the initial population.

P=16000\times 1.1025=17640

You can also verify this year-by-year:

After Year 1:
16000+(5\%\times 16000)=16000+800=16800

After Year 2:
16800+(5\%\times 16800)=16800+840=17640

Notice that in Year 2, the increase is 840 (not 800), because the 5% is now applied to the larger population of 16800. This is the essence of compound growth — the growth builds on itself each period.

Therefore, the population of the city after 2 years will be 17640.