Choose a number greater than 5,000 and less than 10,000 for the value of p.

Question

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. percent -3%

Answer 1

Let's choose a number for \( p \) between 5,000 and 10,000. For this example, we'll choose:

\( p = 7,500 \)

You mentioned a percentage change of -3%. This indicates that we need to decrease the population value by 3%. To find the estimated current population, we can use the following formula:

\[ \text{Current Population} = p \times (1 - \text{percentage change}) \]

In this case, the percentage change is -3%, which as a decimal is -0.03. Therefore, we can rewrite the expression:

\[ \text{Current Population} = p \times (1 - (-0.03)) = p \times (1 - 0.03) = p \times 0.97 \]

Now we can substitute in our value for \( p \):

\[ \text{Current Population} = 7,500 \times 0.97 \]

Now, let's calculate it:

\[ 7,500 \times 0.97 = 7,275 \]

So the estimated current population of Concord is approximately 7,275.

Explanation:

I chose the expression \( p \times 0.97 \) because it effectively adjusts the initial population, \( p \), by taking into account the specified decrease of 3%. The factor \( 0.97 \) represents the remaining percentage of the population after the decrease (100% - 3% = 97%). This method is commonly used in calculations involving percentage changes to quickly find the new value after an increase or decrease.