Assertion (A): The population of a town in 2015 was 10,000. It grew by 10% every year. So, in the year 2020, the population was 15,000.

Reason (R): Formula used in such problems is V = V_o $\Big(1 + \dfrac{r}{100}\Big)^n$

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

The formula, V = V_o $\Big(1 + \dfrac{r}{100}\Big)^n$ is indeed the correct formula used for calculating future value in problems involving compound growth (like population growth, compound interest, etc.), where:

V is the final value.

V_o is the initial value.

r is the rate of growth (or interest) per period.

n is the number of periods.

This formula accurately reflects how a quantity increases by a certain percentage over multiple periods, with the growth compounding on the new total each period.

∴ Reason (R) is true.

Given,

V_o = 10,000

r = 10%.

n = 5 years

Substituting values we get :

$V = 10,000 \times \Big(1 + \dfrac{10}{100}\Big)^5\\[1em] = 10,000 \times \Big(1 + \dfrac{1}{10}\Big)^5\\[1em] = 10,000 \times \Big(\dfrac{10 + 1}{10}\Big)^5\\[1em] = 10,000 \times \Big(\dfrac{11}{10}\Big)^5\\[1em] = 10,000 \times \dfrac{1,61,051}{1,00,000}\\[1em] = 16,105.10$

Since population cannot be in fraction, the population in 2020 would be approximately 16,105.

∴ Assertion (A) is false.

∴ Assertion (A) is false, Reason (R) is true.

Hence, option 2 is the correct option.