Question

Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
Concord p - 5%

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, 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.

Answer 1

Let’s choose the value of \( p \) (the initial population of Concord) to be 7,500, which is greater than 5,000 and less than 10,000.

Concord's population is said to have decreased by 5%. To find the estimated current population, we can use the following expression:

\[
\text{Current population} = p \times (1 + \text{percentage change})
\]

In this case, since the percentage change is a decrease of 5%, we convert this percentage into a decimal:

\[
\text{Percentage change as a decimal} = -0.05
\]

Now, we will set up our calculation:

\[
\text{Current population} = 7,500 \times (1 - 0.05)
\]
\[
= 7,500 \times 0.95
\]
\[
= 7,125
\]

So, the estimated current population of Concord is **7,125**.

### Explanation
We used the expression \( p \times (1 + \text{percentage change}) \) to account for the percentage change in population accurately. Since Concord experienced a decrease, the calculation adjusted the initial population \( p \) down by multiplying it by \( 0.95 \) (which is \( 1 - 0.05 \)). This method is standard when calculating populations or values that undergo percentage changes, ensuring that we account for either increases or decreases correctly. In this case, the decrease led to a straightforward multiplication that allowed us to find the current population.