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.
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