(6) The population density in a circular city depends on the distance r, in km, from the center. The dependence is given by the function f(r) = 10-3r, in thousands of people/km², so that the density is greatest at the center and it is zero at the city limits. Find the radius of the city and its total population. Include units in your answer. Show all your work. Note that the population can be modeled by [2 2πr f(r) dr where r is the radius.
(6) The population density in a circular city depends on the distance r, in km, from the center. The dependence is given by the function f(r) = 10-3r, in thousands of people/km², so that the density is greatest at the center and it is zero at the city limits. Find the radius of the city and its total population. Include units in your answer. Show all your work. Note that the population can be modeled by [2 2πr f(r) dr where r is the radius.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please do number 6
Transcribed Image Text:Find an equation of the line tangent to the graph of y = F(x) at the point x = √e.
Show all your work.
-
(6) The population density in a circular city depends on the distance r, in km, from
the center. The dependence is given by the function
f(r) = 10-3r, in thousands of people/km²,
so that the density is greatest at the center and it is zero at the city limits.
Find the radius of the city and its total population. Include units in your answer.
Show all your work.
Note that the population can be modeled by
2
(7) Consider the region bounded by the graphs of y = e, y = 1 - x, and x = 2.
21
2πrf(r) dr where r is the radius.
(a) Find the area of the region described above by using a midpoint rule with 4
equal subdivisions.
(b) Find the exact area of the region described above.
3
(8) Let P(x) = n(2³) dz. You must show your work to receive credit.
e2x
(a) Find P'(x).
22
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