The volume V of a growing spherical cell is V= r³, where the radius r is measured in micrometers (1 µm = 10-6 m). (a) Find the average rate of change of V with respect to r (in μm³/μm) when r changes from 2 μm to each of the following. (Round your answers to one decimal place.) (1) 2 to 5 μm (II) 2 to 3 μm (ii) 2 to 2.1 μm. um3/um | um3/um lum3/um (b) Find the instantaneous rate of change of V with respect to r (in μm³/μm) when r = 2 μm. (Round your answer to one decimal place.) um³/um

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 51CR
icon
Related questions
Question
The volume V of a growing spherical cell is V = ³, where the radius r is measured in micrometers (1 µm = 10-6 m).
(a) Find the average rate of change of V with respect to r (in μm³/μm) when r changes from 2 μm to each of the following. (Round your answers to one decimal place.)
(1)
2 to 5 µm
(II) 2 to 3 μm
(iii) 2 to 2.1 μm
um3/um
lum3/um
lum3/um
(b) Find the instantaneous rate of change of V with respect to r (in μm³/μm) when r = 2 μm. (Round your answer to one decimal place.)
V'(2) =
lum3/um
Transcribed Image Text:The volume V of a growing spherical cell is V = ³, where the radius r is measured in micrometers (1 µm = 10-6 m). (a) Find the average rate of change of V with respect to r (in μm³/μm) when r changes from 2 μm to each of the following. (Round your answers to one decimal place.) (1) 2 to 5 µm (II) 2 to 3 μm (iii) 2 to 2.1 μm um3/um lum3/um lum3/um (b) Find the instantaneous rate of change of V with respect to r (in μm³/μm) when r = 2 μm. (Round your answer to one decimal place.) V'(2) = lum3/um
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell