1 2.5 4 (centimeters) f(r) 1 10 18 (milligrams per square centimeter) . The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the dish is given by an increasing, differentiable function f, where f(r) is measured in milligrams per square centimeter. Values of f(r) for selected values of r are given in the table above. (a) Use the data in the table to estimate f'(2.25). Using correct units, interpret the meaning of your answer in the context of this problem. (b) The total mass, in milligrams, of bacteria in the petri dish is given by the integral expression 2n | rf(r) dr. Approximate the value of 27 | rf(r) dr using a right Riemann sum with the four subintervals indicated by the data in the table. (c) Is the approximation found in part (b) an overestimate or underestimate of the total mass of bacteria in the petri dish? Explain your reasoning.

1 2.5 4 (centimeters) f(r) 1 10 18 (milligrams per square centimeter) . The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the dish is given by an increasing, differentiable function f, where f(r) is measured in milligrams per square centimeter. Values of f(r) for selected values of r are given in the table above. (a) Use the data in the table to estimate f'(2.25). Using correct units, interpret the meaning of your answer in the context of this problem. (b) The total mass, in milligrams, of bacteria in the petri dish is given by the integral expression 2n | rf(r) dr. Approximate the value of 27 | rf(r) dr using a right Riemann sum with the four subintervals indicated by the data in the table. (c) Is the approximation found in part (b) an overestimate or underestimate of the total mass of bacteria in the petri dish? Explain your reasoning.

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Description: 122.54(centimeters)f(r)121018(milligrams per square centimeter)1. The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of thedish is given by an increasing, differentiable function f, where f(r) i

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic Video

Question

1
2
2.5
4
(centimeters)
f(r)
1
2
10
18
(milligrams per square centimeter)
1. The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the
dish is given by an increasing, differentiable function f, where f(r) is measured in milligrams per square
centimeter. Values of f(r) for selected values of r are given in the table above.
(a) Use the data in the table to estimate f'(2.25). Using correct units, interpret the meaning of your answer
in the context of this problem.
(b) The total mass, in milligrams, of bacteria in the petri dish is given by the integral expression
2л
| rf(r) dr. Approximate the value of 27
rf(r) dr using a right Riemann sum with the four
subintervals indicated by the data in the table.
(c) Is the approximation found in part (b) an overestimate or underestimate of the total mass of bacteria in the
petri dish? Explain your reasoning.
(d) The density of bacteria in the petri dish, for1<rs 4, is modeled by the function g defined by
g(r) = 2 – 16(cos (1.57 F))°. For what value of k, 1 < k < 4, is g(k) equal to the average value of g(r)
on the interval 1 < r < 4 ?

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