Imagine a very crowded large city, with each person standing on his or her own 2-foot-by-2-foot square, where the squares are adjacent. Calculate the population density per square mile. (1 mile = 5,280 feet) Try the problem on your own first. If you are having trouble after 2 tries, we will break it down. Population density: people per square mile Question Help: Message instructor Submit Question Question 8 Imagine an average city like Lakewood or Puyallup, where each person could stand on his or her own 100-foot- by-100-foot square. Calculate the population density per square mile, to the nearest whole person. people per square mile Question Help: Message instructor Submit Question
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In Lakewood or Puyallup, this would be 9,000 people. Show more…
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Population Density Population density measures the number of people per square mile inhabiting a given living area. Washerton's population density, which decreases as you move away from the city center, can be approximated by the function $10,000(2-r)$ at a distance $r$ miles from the city center.(a) If the population density approaches zero at the edge of the city, what is the city's radius? (b) A thin ring around the center of the city has thickness $\Delta r$ and radius $r$ . If you straighten it out, it suggests a rectangular strip. Approximately what is its area? (c) Writing to Learn Explain why the population of the ring in part (b) is approximately $$10,000(2-r)(2 \pi r) \Delta r$$ (d) Estimate the total population of Washerton by setting up and evaluating a definite integral.
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