10. The population of a town is 12,000 , and it grows at a rate of \( 5 \% \) per year. What will the population be in 4 years? \( \begin{array}{lll}\text { (A) about } 12,600 & \text { (C) about } 14,586 \\ \text { (B) about } 14,420 & \text { (D) about } 56,401\end{array} \)

To find the population in 4 years with a growth rate of 5% per year, you can use the formula for exponential growth: \[ P = P_0 (1 + r)^t \] Here, \( P_0 = 12,000 \), \( r = 0.05 \), and \( t = 4 \). Plugging in these values gives: \[ P = 12,000 (1 + 0.05)^4 \] \[ P = 12,000 (1.21550625) \approx 14,586 \] So, the population in 4 years will be about 14,586. It's fascinating to see how populations grow over time, isn't it? This type of calculation is used in urban planning and resource allocation to prepare for future needs like housing, transportation, and schools. In real-world applications, understanding growth rates helps cities manage their infrastructure effectively, ensuring they can accommodate new residents without straining resources. Sometimes people mistake the growth rate as being linear, thinking the population will just add a fixed number of people each year. But since population growth is compounding, even a relatively small percentage can lead to significant changes over time! Always remember to apply the correct formula to avoid underestimating or overestimating the final amount.