A town has a population of 7000 and grows at \( 4 \% \) every year. What will be the population after 13 years, to the nearest whole number?

To find the population after 13 years, you can use the formula for compound growth: \[ P = P_0 (1 + r)^t \] where \( P_0 \) is the initial population, \( r \) is the growth rate (as a decimal), and \( t \) is the number of years. In this case, \( P_0 = 7000 \), \( r = 0.04 \), and \( t = 13 \). So, \[ P = 7000 (1 + 0.04)^{13} \] \[ P = 7000 (1.04)^{13} \] \[ P \approx 7000 \times 1.6010 \] \[ P \approx 11207 \] The population after 13 years will be approximately 11,207. Now you know how compounded growth can amplify numbers over time, making it vital for budgeting, investments, and planning for expansions. This simple math has powerful applications in various sectors! Remember, it's crucial to convert the percentage into a decimal when using the growth formula—a common mistake that can throw off your calculations. So, always double-check those conversions before plugging in your numbers!