A town's population increased from 14,523 to 16,489. What is the percent increase in the town's population? Round to the nearest percent.
To find the percentage increase in the town's population, we first identify the initial and final values. The initial population is \(P_{\text{initial}} = 14,523\) and the final population is \(P_{\text{final}} = 16,489\). The percentage increase formula is given by:
\[\text{Percent Increase} = \left( \frac{P_{\text{final}} - P_{\text{initial}}}{P_{\text{initial}}} \right) \times 100\%\]
This formula allows us to determine the relative change of the population compared to its starting size.
Next, we calculate the absolute increase in population:
\[\Delta P = P_{\text{final}} - P_{\text{initial}} = 16,489 - 14,523 = 1,966\]
Now, we divide this absolute increase by the initial population:
\[R = \frac{1,966}{14,523} \approx 0.13537\]
Finally, we convert this ratio to a percentage by multiplying by 100:
\[P_{\%} = 0.13537 \times 100\% = 13.537\%\]
Rounding this to the nearest whole percent, we obtain 14%.
Understanding percentage increase is a fundamental skill in everyday life, used to track changes in things like investments, savings, or data trends. For example, if you track the growth of your monthly savings or the increase in the number of books you have read over a year, you can use this exact method to express your progress as a percentage. It helps in making informed decisions about how your resources are changing over time.