Math

CalculusCalculusBacteria Growth At time t = 0 . a bacterial culture weighs 1 gram. Two hours later, the culture weighs 4 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (b) Find the culture’s weight after 5 hours. (c) When will the culture’s weight reach 18 grams? (d) Write a logistic differential equation that models the growth rate of the culture’s weight. Then repeat part (b) using Euler’s Method with a step size of h = 1 . Compare the approximation with the exact answer. (e) At what time is the culture’s weight increasing most rapidly? Explain.BuyFind*launch*

10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 6.3, Problem 60E

Textbook Problem

**Bacteria Growth** At time

(a) Write a logistic equation that models the weight of the bacterial culture.

(b) Find the culture’s weight after 5 hours.

(c) When will the culture’s weight reach 18 grams?

(d) Write a logistic differential equation that models the growth rate of the culture’s weight. Then repeat part (b) using Euler’s Method with a step size of

(e) At what time is the culture’s weight increasing most rapidly? Explain.

Calculus

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The functions f and g are both...Ch. 6.2 - Modeling Data The table shows the resident...Ch. 6.2 - Forestry The value of a tract of timber is...Ch. 6.2 - Sound Intensity The level of sound (in decibels)...Ch. 6.2 - Noise Level With the installation of noise...Ch. 6.2 - Newton's Law of Cooling When an object is removed...Ch. 6.2 - Newton's Law of Cooling A container of hot liquid...Ch. 6.2 - True or False? In Exercises 6770, determine...Ch. 6.2 - True or False? In Exercises 6770, determine...Ch. 6.2 - True or False? In Exercises 67 and 68, determine...Ch. 6.2 - True or False? In Exercises 6770, determine...Ch. 6.3 - Mutually Orthogonal What does it mean for two...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Finding a Particular Solution In Exercises 2528,...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Using Slope In Exercises 33 and 34, find all...Ch. 6.3 - Using Slope In Exercises 33 and 34, find all...Ch. 6.3 - Slope Field In Exercises 31 and 32, sketch a few...Ch. 6.3 - Slope Field In Exercises 31 and 32, sketch a few...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Radioactive Decay The rate of decomposition of...Ch. 6.3 - Chemical Reaction In a chemical reaction a certain...Ch. 6.3 - Weight Gain A calf that weighs 60 pounds at birth...Ch. 6.3 - Weight Gain A calf that weighs w0 pounds at birth...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises 4146,...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Using a Logistic Equation In Exercises 53 and 54,...Ch. 6.3 - Using a Logistic Equation In Exercises 53 and 54,...Ch. 6.3 - Using a Logistic Differential Equation In...Ch. 6.3 - Using a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Endangered Species A conservation organization...Ch. 6.3 - Bacteria Growth At time t=0. a bacterial culture...Ch. 6.3 - Separation of Variables In your own words,...Ch. 6.3 - Finding a Derivative Show that if y=11+bekt, then...Ch. 6.3 - Point of Inflection For any logistic equation,...Ch. 6.3 - Sailing Ignoring resistance, a sailboat starting...Ch. 6.3 - HOW DO YOU SEE IT? The growth of a population is...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - True or False? In Exercises 83-85, determine...Ch. 6.3 - True or False? In Exercises 83-85, determine...Ch. 6.3 - True or False? 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In Exercises 65 and 66, determine...Ch. 6.4 - True or False? In Exercises 65 and 66, determine...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Air Pressure Under ideal conditions, air pressure...Ch. 6 - Radioactive Decay Radioactive radium has a...Ch. 6 - Population A population grows exponentially at a...Ch. 6 - Compound Interest Find the balance in an account...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Slope Field In Exercises 41 and 42, sketch a few...Ch. 6 - Slope Field In Exercises 41 and 42, sketch a few...Ch. 6 - Using a Logistic Equation In Exercises 47 and 48,...Ch. 6 - Using a Logistic Equation In Exercises 47 and 48,...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Environment A conservation department releases...Ch. 6 - Environment Write a logistic differential equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Finding a Particular Solution In Exercises 59-62,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Doomsday Equation The differential equation...Ch. 6 - Sales Let S represent sales of a new product (in...Ch. 6 - Gompertz Equation Another model that can be used...Ch. 6 - Error Using the Product Rule Although it is true...Ch. 6 - Torricelli's Law Torricellis Law states that water...Ch. 6 - Torricelli's Law The cylindrical water tank shown...Ch. 6 - Torricelli's Law A tank similar to the one in...Ch. 6 - Rewriting the Logistic Equation Show that the...Ch. 6 - Biomass Biomass is a measure of the amount of...Ch. 6 - If the tracer is injected instantaneously at time...Ch. 6 - Use the solution of the differential equation in...Ch. 6 - In Exercises 11 and 12, it was assumed that there...

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Find all elements of the subgroup generated by the given . ...

Elements Of Modern Algebra

Use Figure 22 for Problems 31 through 34. Figure 22 Find a ratio that is equivalent to xy.

Trigonometry (MindTap Course List)

is a(n):
ellipsoid
elliptic cone
elliptic paraboloid
elliptic cylinder

Study Guide for Stewart's Multivariable Calculus, 8th

A circle is increasing in area at 4 cm2/min. How fast is the radius changing when the radius is 10 cm?
cm/min...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Volume In Exercises 27 and 28, use a double integral in polar coordinates to find the volume of the solid bound...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 21 to 26, find the measures of the angles named to the nearest degree.

Elementary Geometry for College Students

FINANCING A CAR Darla purchased a new car during a special sales promotion by the manufacturer. She secured a l...

Finite Mathematics for the Managerial, Life, and Social Sciences

Line Integral of a Conservative Vector Field In Exercises 45 and 46, (a) show that F is conservative and (b) ve...

Multivariable Calculus

Draw a graph with four vertices: all of degree 3.

Mathematics: A Practical Odyssey

Represent the decimal integers in 1-6 in binary notation. 1424

Discrete Mathematics With Applications

Add the terms in the following expressions. 50.6abc+50.5abc

Mathematics For Machine Technology

Decompose each fraction into partial fractions. x3x2+3x+2

College Algebra (MindTap Course List)

Compute the price relatives for the RB Beverages products in exercise 4. Use a weighted average of price relati...

Statistics for Business & Economics, Revised (MindTap Course List)

An Aluminum Can, Continued This is a continuation of Exercise 12. The cost of making a can is determined by how...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Identify the statistical analyses that are appropriate to evaluate the mean differences for two-factor designs,...

Research Methods for the Behavioral Sciences (MindTap Course List)

Data on quantities of three items sold in Year 1 and Year 5 are given here along with the sales prices of the i...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A social science researcher would like to determine the characteristics of people who live and work in small to...

Research Methods for the Behavioral Sciences (MindTap Course List)

Groundwater is the main source of water in many countries. In a study of the quality of ground water in Yemen, ...

Introduction To Statistics And Data Analysis

40. The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a produc...

Essentials Of Statistics For Business & Economics

In Problems 25-30 solve the given initial-value problem. Use a graphing utility to graph the solution curve. 28...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Consider the following hypothesis test:
A sample of 40 provided a sample mean of 26.4. The population standard...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Improper Rational Expression Decomposition In Exercises 43-50, write the partial fraction decomposition of the ...

College Algebra

For the following exercises, P is a point on the unit circle. a. Find the (exact) missing coordinate value of e...

Calculus Volume 1

Use the following information to answer the next two exercises. An experiment is conducted to show that blood p...

Introductory Statistics

Find the derivative. 455. ddt0tsinx 1+ x 2 dx

Calculus Volume 2