Explanation
$${\textbf{Step - 1: Framing the formula for finding the rate of decrease}}{\text{.}}$$
$${\text{Let the rate of increase in the population be }}r,$$
$${\text{We know, population increases geometrical progression so, we}}$$
$${\text{will use the compound interest formula}}{\text{.}}$$
$${\text{Given}},{\text{ }}P{\text{ }} = {\text{ }}16,000$$
$${\text{Time period }},{\text{ }}n{\text{ }} = {\text{ }}2$$
$${\text{Population after }}2{\text{ yrs }},{\text{ }}A{\text{ }} = {\text{ }}17640$$
$${\text{Using the formula of compound interest, we can write}}$$
$$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$$
$$17640 = 16000{\left( {1 + \dfrac{r}{{100}}} \right)^2}$$
$${\textbf{Step - 2: Solving the above equation to find the rate of decrease}}{\text{.}}$$
$$\dfrac{{17640}}{{16000}} = {\left( {1 + \dfrac{r}{{100}}} \right)^2}$$
$$\dfrac{{441}}{{400}} = {\left( {1 + \dfrac{r}{{100}}} \right)^2}$$
$${\text{Taking square root on both the sides,}}$$
$$\dfrac{{21}}{{20}} = 1 + \dfrac{r}{{100}}$$
$$\dfrac{1}{{20}} = \dfrac{r}{{100}}$$
$$r = 5% $$
$${\textbf{Hence, the rate of decrease of population is 5% }}{\text{.}}$$
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