Choose a number greater than 5,000 and less than 10,000 for the value of p. Based on the percentage change you chose in part b) above, calculate the estimated current population of Concord, rounding to the nearest whole number if needed. Explain why you used the expression you did to make your calculation.

Question

GPT-4o mini · Answer

Let’s choose a value for $ p $ in the range of 5,000 to 10,000. For example, let’s select $ p = 7,500 $. Now, suppose in part b you chose a percentage change of, say, 10% (for illustration purposes). To find the estimated current population, we can use the formula for population change: $$ \text{Estimated current population} = p + (p \times \text{percentage change}) $$ Using a percentage change of 10% as a decimal, which is 0.10: $$ \text{Estimated current population} = 7500 + (7500 \times 0.10) $$ Calculating it: $$ = 7500 + (7500 \times 0.10) $$ $$ = 7500 + 750 $$ $$ = 8250 $$ Therefore, the estimated current population of Concord would be **8,250**. ### Explanation I used the expression $ p + (p \times \text{percentage change}) $ to calculate the estimated current population because it effectively accounts for a percentage increase (or decrease) from the initial value $ p $. This formula combines the base population with the absolute change calculated from the percentage increase, providing a straightforward way to determine the new population size based on the selected percentage change.