6. The function \( P(t)=5,000(1.015)^{t} \) is time in years since 2010 . What does the value of \( P(7) \) mean in terms of A. Springfield has a population of 5,549 people in 2007 . B. Springfield has a population of 5,549 people in 2017 . C. Springfield has a population of 35,525 people in 2007 . D. Springfield has a population of 35,525 people in 2017 .

To find \( P(7) \), we substitute \( t = 7 \) into the function: \[ P(7) = 5,000(1.015)^{7} \approx 5,000(1.107) \approx 5,535. \] This calculation gives us around 5,535, which represents the projected population of Springfield in 2017 since \( t = 7 \) corresponds to 2017 when considering the base year as 2010. Thus, option B is the correct interpretation. In terms of context, Springfield's population growth can be attributed to various factors like economic opportunities, migration, and birth rates—much like the way other regions experience demographic changes over time! By analyzing such data, cities can plan better for future needs. Furthermore, understanding how the exponential growth function models changes in populations, businesses, or even viral trends can help in strategizing future decisions. It’s like using a crystal ball that predicts the future based on current trends!