Concept explainers
a.
To calculate city’s radius if the population density approaches zero at the edge of the city.
a.
Answer to Problem 23E
The radius of the city is 2 miles.
Explanation of Solution
Given information:
The decrease in Washerton’s population density as you move away from the city can be approximated by the function
Calculation:
Calculation density at end of the city is zero.
Therefore, The radius of the city is 2 miles.
b.
To state the approximate area.
b.
Answer to Problem 23E
The area is
Explanation of Solution
Given information:
Radius of the ring is r and its thickness is
If the ring is straighten out the circumference of the ring become the length of the rectangle and its thickness becomes breadth of the rectangle.
Therefore,
The area is
c.
To explain why the population of the ring in part (b) is approximately
c.
Answer to Problem 23E
Explanation of Solution
Given information:
Radius of the ring is r and its thickness is
The population of the ring is
And
d.
To estimate the total population of Washerton by setting up and evaluating a definite integral.
d.
Answer to Problem 23E
The population is approximately 83,776
Explanation of Solution
Given information:
The population density function is
Calculation:
Since the radius is evaluated as 2 miles.
Seek the cumulative effect of population density for
The population is
Therefore,
The population is approximately 83,776
Chapter 8 Solutions
Calculus: Graphical, Numerical, Algebraic
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