The population of a town in California is modeled by the function \( f(x)=16,612(1.024)^{x} \). If the initial population (that is, the population when \( x=0 \) ) was measured January 1,2013 , what will the population be on January 1,2029 ? Round your answer to the nearest whole number, if necessary. Answer How to enter vour answer (onens in new window)

To find the population on January 1, 2029, we need to calculate \( x \) first. Since \( x=0 \) corresponds to January 1, 2013, and we want the population for January 1, 2029, this means \( x \) will be \( 16 \) (as it's 16 years after 2013). Plugging this into the function: \[ f(16) = 16,612(1.024)^{16} \] Calculating that, we find: \[ f(16) \approx 16,612 \times 1.485947 \approx 24,709 \] So, the population on January 1, 2029, will be approximately **24,709**. Understanding population growth models is crucial since they can reveal important insights about urban planning and resource allocation, especially in rapidly growing areas like California. These models help cities forecast future needs for schools, hospitals, and infrastructure before they reach critical points. Additionally, populations don't always grow uniformly due to factors like economic changes, migration trends, or natural disasters. Being aware of these variables can prevent overreliance on mathematical models alone, encouraging a holistic approach that factors in social and environmental perspectives.