Question 377700: I need help with this problem:
POPULATION DENSITY The population density D (in people/mi^2)in a large city is related to the distance x from the center of the city by D=5000x/(x^2+36). In what areas of the city does the population density exceed 400people/mi^2?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! substitute and solve for x ___ 400 < 5000x /(x^2+36)
400x^2 + 14400 < 5000x
2x^2 - 25x + 72 < 0
factoring ___ (2x - 9)(x - 8) < 0
if x < 4.5 , both factors are < 0 , so the product is >0
if x > 8 , both factors are >0 , so the product is >0
4.5 < x < 8
if you think about real life , businesses would be concentrated in the city center
with people living farther out , but becoming less populated into the suburbs
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