Final answer:
The equation modeling the city's population growth is p = 4x + 390, where p is the population (in thousands) and x is the number of years after 2010.
Step-by-step explanation:
The equation that gives the city's population p (in thousands of people) x years after 2010 is p = 40000x + p₀, where p₀ is the population of the city in the year 2010. To find p₀, we use the given information that the population in 2025 (15 years after 2010) is projected to be 450,000 people. The increase over 15 years is 15 × 4,000 = 60,000 (in thousands). If we subtract this increase from the 2025 population, we obtain the population in 2010: 450,000 - 60,000 = 390,000 (in thousands). Therefore, the population of the city in 2010 was 390,000 people, and the equation modeling the population x years after 2010 is p = 4x + 390, where p is in thousands and x is the number of years after 2010.