To calculate the estimated current population of Concord using your specified value of \( p = 6742 \) and a percentage change of \(-3%\), we will first find the original population before the decrease.
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Understanding the percentage change: A percentage change of \(-3%\) means the population decreased by 3%. Therefore, the current population can be represented as: \[ \text{Current Population} = p \times (1 - \text{Percentage Change}) \] Here, the percentage change is \(-3%\), which we convert to a decimal by dividing by 100: \[ 1 - (-0.03) = 1 - 0.03 = 0.97 \]
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Setting up the equation: Now substituting the chosen population \( p = 6742 \) into the equation: \[ \text{Current Population} = 6742 \times 0.97 \]
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Calculating the estimated current population: \[ \text{Current Population} = 6742 \times 0.97 = 6539.74 \]
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Rounding to the nearest whole number: Rounding \( 6539.74 \) gives us approximately: \[ \text{Current Population} \approx 6540 \]
Explanation of the expression used:
The expression \( p \times (1 - \text{Percentage Change}) \) is used because it effectively calculates the new value after a percentage decrease. The term \( (1 - \text{Percentage Change}) \) represents the remaining percentage of the original population after accounting for the decrease. Multiplying by \( p \) gives us the current population after the specified decrease.
Thus, the estimated current population of Concord, based on your numbers, is approximately 6540 people.
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