Question

The population density, D, in people/square mile (p/mi²), for the large city Westport is related to the distance x (in miles) from the city’s center by the equation:________.

D=4300x /x^2 + 40.
a. Describe what happens to West-port's population density as the distance from the city’s center changes from one mile to six miles. What may explain this phenomenon?
b. Describe what happens to West-port's population density as the distance from the city’s center changes from ten miles to thirty miles.
c. Describe the end-behavior of this function? What may explain this phenomenon?
d. In what areas of the city is the population density below 200 p/mi²?

Answer 1

Explanation:

D=4300x /x² + 40.

x = 1

D = 4300 / 41 = 104.88 p / mi²

x = 6

D = 25800 / 76

= 339.47 p / mi²

Population density increases as we go away from city's centre .

b )

x = 10

D=4300x /x² + 40.

D = 307.14 p/ mi²

x = 30

D = 137.23 p / mi²

Population decreases .

c )

when x is very high , density will decrease due to squared denominator whose value increases very fast .

d )

D < 200

4300x /x² + 40 < 200

4300 x < 200 x² + 8000

43 x < 2 x² + 80

2 x² - 43 x + 80 > 0

( x - 19.44 ) ( x - 2.05 ) > 0

Range x < 2.05

x > 19.44