Final answer:
The growth curve for urban expansion into rural areas is likely S-shaped, characterized by initial rapid growth that slows over time as space and resources become limited, following the rural-to-urban population shift and trends in economic development.
Step-by-step explanation:
The shape of the growth curve for a scenario in which cities extend into rural countryside is likely to reflect a significant rural-to-urban population shift. The growth curve of a city or metropolitan area expanding into the countryside would typically represent an S-shaped logistic growth curve, where rapid growth is eventually tempered as space becomes more limited and resources become scarcer. Initially, as urban areas start to spread, there's a high rate of growth, driven by opportunities and advantages in urban centers that attract people from rural areas. However, as the urban area expands and the surrounding countryside becomes more developed, the rate of growth slows down. This slowing down aligns with stage 3 of the index of economic development, where a rural-to-urban shift occurs as populations move towards cities, and subsequently, when family size starts to decrease, and incomes begin to rise. As more regions reach stage 5, with high income levels and smaller family sizes, the growth pattern stabilizes and the growth rate diminishes. Hence, the growth curve exhibits a leveling off as space for expansion decreases and population stabilizes.