State true/false:

The population of the city was 20,000 in the year 1997. It increased at the rate of 5% p.a. The population at the end of the year 2000 would be 23553.

The given statement is false.

Every year, there is a 5% increase in population, so every new year has a new population. Thus, we can say it is increasing in compounded form.

Where n is the number of years after 1997.

So, for the end of the year 2000, n = 3.

The population at the end of the year 2000 = $20000{\left(1+\frac{5}{100}\right)}^3$

$=20000\times {\left(\frac{21}{20}\right)}^3$

$=20000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}$

= 23152.5

So, the estimated population at the end of the year 2000 = 23153.