The infrastructure needs of a region (for example, the number of miles of electrical cable, the number of miles of roads, the number of gas stations) depend on its population. Cities enjoy economies of scale. For example, the number of gas stations is proportional to the population raised to the power of 0.77.
(a) Write a formula for the number, N, of gas stations in a city as a function of the population, P, of the city.
(b) If city A is 10 times bigger than city B, how do their number of gas stations compare?
(c) Which is expected to have more gas stations per person, a town of 10,000 people or a city of 500,000 people?