- Round the initial population \(12,089\) to \(12,000\) and the final population \(15,025\) to \(15,000\).
- Apply the percent increase formula: \(\frac{15,000 - 12,000}{12,000} \times 100\%\).
- Simplify the expression: \(\frac{3,000}{12,000} \times 100\% = 0.25 \times 100\% = 25\%\).
- The correct option is \(\boxed{b}\).
Explanation
- Rounding the Populations
We are given an initial town population of \(12,089\) and a final population of \(15,025\). To estimate the percent increase, we must first round both population figures to the nearest thousand.
- The initial population is \(12,089\). Since \(089\) is less than \(500\), we round down to \(12,000\).
- The final population is \(15,025\). Since \(025\) is less than \(500\), we round down to \(15,000\).
- Calculating the Percent Increase
Now that we have our rounded population values, we use the percent increase formula:
\[\text{Percent Increase} = \left(\frac{\text{Final} - \text{Initial}}{\text{Initial}}\right) \times 100\%\]
Substituting the rounded values \(12,000\) and \(15,000\) into the formula, we get:
\[\text{Percent Increase} = \left(\frac{15,000 - 12,000}{12,000}\right) \times 100\%\]
\[\text{Percent Increase} = \left(\frac{3,000}{12,000}\right) \times 100\%\]
- Conclusion
Simplifying the fraction \(\frac{3,000}{12,000}\):
\[\frac{3,000}{12,000} = \frac{3}{12} = \frac{1}{4} = 0.25\]
Multiplying by \(100\%\) gives:
\[0.25 \times 100\% = 25\%\]
Comparing this to the given choices, we see that the correct approximation is \(25\%\), which corresponds to option (b). The final result is \(\boxed{b}\).
Examples
Understanding how to estimate percent change is a vital skill in many real-life situations. For example, if you are tracking the growth of your savings or the increase in the price of groceries over a year, you can use rounding to get a quick estimate of how much your money has grown or depreciated. This allows for quick, mental calculations to understand trends without needing exact, precise figures every time.