Chapter 3, Problem 93RE
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Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270343
Solutions
Chapter
Section
BuyFindarrow_forward
Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem
A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells.
(a) Find the number of bacteria after t hours.
(b) Find the number of bacteria after 4 hours.
(c) Find the rate of growth after 4 hours.
(d) When will the population reach 10,000?
(a)
To determine
To find: The number of bacteria after t hours.
Explanation
Theorem used:
“The only solutions of the differential equation
Calculation:
Let
The bacteria culture initially contains 200 cells. That is,
After half hour the population increased to 360,
Since the rate of the population of the bacteria is proportional to its size,
By theorem stated above,
Substitute
Substitute
(b)
To determine
To find: The number of bacteria after 4 hours is
(c)
To determine
To find: The rate of growth after 4 hours.
(d)
To determine
To find: The time at which population reach 10,000.
Chapter 3 Solutions
Sect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10E
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P-57ESect-3.11 P-58ECh-3 P-1RCCCh-3 P-2RCCCh-3 P-3RCCCh-3 P-4RCCCh-3 P-5RCCCh-3 P-6RCCCh-3 P-7RCCCh-3 P-1RQCh-3 P-2RQCh-3 P-3RQCh-3 P-4RQCh-3 P-5RQCh-3 P-6RQCh-3 P-7RQCh-3 P-8RQCh-3 P-9RQCh-3 P-10RQCh-3 P-11RQCh-3 P-12RQCh-3 P-13RQCh-3 P-14RQCh-3 P-15RQCh-3 P-1RECh-3 P-2RECh-3 P-3RECh-3 P-4RECh-3 P-5RECh-3 P-6RECh-3 P-7RECh-3 P-8RECh-3 P-9RECh-3 P-10RECh-3 P-11RECh-3 P-12RECh-3 P-13RECh-3 P-14RECh-3 P-15RECh-3 P-16RECh-3 P-17RECh-3 P-18RECh-3 P-19RECh-3 P-20RECh-3 P-21RECh-3 P-22RECh-3 P-23RECh-3 P-24RECh-3 P-25RECh-3 P-26RECh-3 P-27RECh-3 P-28RECh-3 P-29RECh-3 P-30RECh-3 P-31RECh-3 P-32RECh-3 P-33RECh-3 P-34RECh-3 P-35RECh-3 P-36RECh-3 P-37RECh-3 P-38RECh-3 P-39RECh-3 P-40RECh-3 P-41RECh-3 P-42RECh-3 P-43RECh-3 P-44RECh-3 P-45RECh-3 P-46RECh-3 P-47RECh-3 P-48RECh-3 P-49RECh-3 P-50RECh-3 P-51RECh-3 P-52RECh-3 P-53RECh-3 P-54RECh-3 P-55RECh-3 P-56RECh-3 P-57RECh-3 P-58RECh-3 P-59RECh-3 P-60RECh-3 P-61RECh-3 P-62RECh-3 P-63RECh-3 P-64RECh-3 P-65RECh-3 P-66RECh-3 P-67RECh-3 P-68RECh-3 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For what values of x is f continuous? f(x)={0ifxisrational1ifxisirrational
Single Variable Calculus: Early Transcendentals
Solve the following equations for x if 0x2. Use a calculator to approximate all answers to the nearest hundredt...
Trigonometry (MindTap Course List)
True or False Label each of the following statements as either true or false. 8. A unity exists in any commut...
Elements Of Modern Algebra
With ABDCBE and A-D-E-C, does it necessarily Follow that AEB and CDB are congruent?
Elementary Geometry For College Students, 7e
John Rock has narrowed down his selection of a new cell phone to two models with similar features. Model 800 is...
Contemporary Mathematics for Business & Consumers
Using Illustration 1, solve each right triangle: ILLUSTRATION 1 B=9.45,a=1585ft
Elementary Technical Mathematics
Using Rolles Theorem In Exercises 11-24, determine whether Rolles Theorem can be applied to f on the closed int...
Calculus of a Single Variable
Using partial Fractions In Exercises 3-20, use partial fractions to find the indefinite integral. x2x42x28dx.
Calculus: Early Transcendental Functions (MindTap Course List)
INPUT-OUTPUT MATRICES The matrix A=[0.10.30.40.30.10.20.20.10.3] is an input-output matrix associated with a n ...
Finite Mathematics for the Managerial, Life, and Social Sciences
In Exercises 37 to 40, use induction to state a conclusion. Several movies directed by Lawrence Garrison have w...
Elementary Geometry for College Students
Sometimes, Always, or Never: If for all n and both {an} and {cn} converge, then{bn} converges.
Study Guide for Stewart's Multivariable Calculus, 8th
Curvature at the PoleIn Exercises 73 and 74, use the result of Exercise 72 to find the curvature of the rose cu...
Multivariable Calculus
Finding the Unit Tangent Vector In Exercises 3-8, find the unit tangent vector to the curve at the specified va...
Calculus (MindTap Course List)
f(x) = (x2 3)2 has points of inflection at x = _____. a) 0,3,3 b) 1, 1 c) 0, 1, 1 d) 3,3
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
As part of a study to determine the effects of allowing the use of credit cards for alcohol purchases in Canada...
Introduction To Statistics And Data Analysis
For Exercises 3336, let U={xxisthenameofoneofthestatesintheUnitedStates} A={xxUandxbeginswiththeletterA} I={xxU...
Mathematics: A Practical Odyssey
Describe the goal of single-case research and explain how single-case designs are related to other experimental...
Research Methods for the Behavioral Sciences (MindTap Course List)
Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal...
Mathematics For Machine Technology
In addition to the key words, you should also be able to define the following terms: Third-variable problem Pla...
Research Methods for the Behavioral Sciences (MindTap Course List)
The Wall Street Journal/Harris Personal Finance poll asked 2082 adults if they owned a home (All Business websi...
Statistics for Business & Economics, Revised (MindTap Course List)
Applications: Area of an ellipse The area A of the ellipse x2a2+y2b=1 is given by A=ab. Find the area of the el...
College Algebra (MindTap Course List)
An automotive part must be machined to close tolerances to be acceptable to customers. Production specification...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
