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 calculate the population after 13 years with an initial population of 7000 growing at 4% per year, you can use the formula for exponential growth: \[ P = P_0(1 + r)^t \] where \( P_0 \) is the initial population, \( r \) is the growth rate (0.04), and \( t \) is the time in years (13). Using this formula: \[ P = 7000(1 + 0.04)^{13} \] Calculating it step by step gives: \[ P = 7000(1.04)^{13} \] \[ P \approx 7000 \times 1.6007 \approx 11205 \] So, the population after 13 years, rounded to the nearest whole number, is about 11,205. Now let's see how this situation unfolds in real-life scenarios and what common mistakes might occur when performing such calculations: Growing populations can put a strain on local resources and infrastructure, leading towns to plan for additional services such as schools, roads, and healthcare. Ensuring that growth is sustainable while maintaining a high quality of life can be a challenge for town planners, making accurate projections vital for future developments and budgeting. When calculating population growth, a common mistake is forgetting to convert percentage rates into decimal form (e.g., using 4 as opposed to 0.04). Additionally, some might misapply the formula by not recognizing it as exponential growth, resulting in incorrect linear projections instead. Always double-check the formula and your rate conversion!