To find the population of the town in January 2000, given that it was 240,000 in January 1998 and increased by 2% each year, we can use the formula for compound interest, which is also applicable for population growth. The formula is: \[ P = P_0 (1 + r)^t \] Where: - \( P \) is the future population. - \( P_0 \) is the initial population. - \( r \) is the growth rate (as a decimal). - \( t \) is the number of years. ### Step-by-Step Calculation 1. **Identify the Variables**: - Initial population, \( P_0 = 240,000 \) - Growth rate, \( r = 2\% = 0.02 \) - Time period, \( t = 2 \) years (from January 1998 to January 2000) 2. **Plug the Values into the Formula**: \[ P = 240,000 \times (1 + 0.02)^2 \] 3. **Calculate \( (1 + 0.02) \)**: \[ 1 + 0.02 = 1.02 \] 4. **Raise \( 1.02 \) to the power of 2**: \[ (1.02)^2 = 1.02 \times 1.02 = 1.0404 \] 5. **Multiply by the Initial Population**: \[ P = 240,000 \times 1.0404 \] \[ P = 249,696 \] Thus, the population of the town in January 2000 is **249,696**. ### Explanation of the Correct Option The correct answer is **B. 249,696**. This is derived from applying the compound growth formula correctly, taking into account the annual growth rate and the number of years. ### Explanation of Why Other Options Are Incorrect - **A. 480,000**: This option suggests that the population doubled, which would only happen with a 100% increase, not a 2% increase over two years. - **C. 249,600**: This option is close but incorrect. It seems to be a miscalculation, possibly from incorrectly applying the growth rate or rounding prematurely. - **D. 244,800**: This option is also incorrect. It may result from misunderstanding the growth calculation or using a wrong formula. ### Common Pitfalls - **Rounding too early**: Always perform calculations with full precision before rounding the final answer. - **Misunderstanding the growth rate**: Remember that a 2% increase means multiplying by 1.02, not adding 2% directly to the population. - **Forgetting to apply the formula correctly**: Ensure you understand the components of the formula and how they relate to the problem. ### Revision Summary - Use the compound growth formula \( P = P_0 (1 + r)^t \) for population growth. - Convert percentage growth rates to decimals (e.g., 2% = 0.02). - Calculate the growth factor for the number of years and multiply by the initial population. - Be cautious of rounding and ensure calculations are done accurately before arriving at the final answer.