The population of the town of Nadiad was 150,000 in 2018 and 165,000 in 2022. What is the average annual growth rate (in %)?

medium 4 marks Class 9 · Geography · Population

Answer

2.42%

The correct answer is 2.42% — Step 5: Convert to percentage: $0.0242 \times 100 = 2.42$ .

Step-by-step solution

Step 1: Identify the initial population $P_{0} = 150, 000$ and the final population $P_{n} = 165, 000$ .
Step 2: Compute the ratio $\frac{P _{n}}{P _{0}} = \frac{165 , 000}{150 , 000} = 1.10$ .
Step 3: Find the 4th root (since the period is 4 years) using $(1.10)^{1/4} a pp r o x 1.0242$ .
Step 4: Subtract 1 to get the growth factor: $1.0242 - 1 = 0.0242$ .
Step 5: Convert to percentage: $0.0242 \times 100 = 2.42$ .

Common mistake: Using the formula

\frac{P _{n} - P _{0}}{P _{0} \times n}

instead of the root method.

Concept tested: Average annual growth rate calculation.