Use the following information to answer the subsequent questions. A simple monocentric city Roundville) has a population of 3,000,000 with a homogeneous density of 5 inhabitants per acre, and one person per household. Agricultural rents are $500/acre/yr, housing construction costs including developer profit) can be paid for with a perpetual loan charging interest of $5000/house/yr, and transportation costs are $250/person/yr per mile of distance from the center of the city. Recall that there are 640 acres per Mi 2 .)
-What is the annual transportation cost per household at the edge of Roundville?

Question

Quizplus · Accepted Answer

To find the annual transportation cost per household at the edge of Roundville, we first need to determine the radius of the city. With a population of 3,000,000 and a density of 5 inhabitants per acre, the total area in acres is 3,000,000 / 5 = 600,000 acres. Since there are 640 acres per square mile, the area in square miles is 600,000 / 640 = 937.5 square miles. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Solving for r gives us r = sqrt(A/π) = sqrt(937.5/π) ≈ 17.3 miles. The annual transportation cost per household at the edge (17.3 miles from the center) is 17.3 miles * $250/mile/person = $4,325. Since the options are rounded, the closest option is D) $4,320.

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