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6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 6.4, Problem 32E

Textbook Problem

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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) After how many hours is the culture’s weight increasing most rapidly? Explain.

**(a)**

To determine

**To calculate:** The logistic equation that models the weight of the bacteria culture where the pattern is given as follows:

At time

**Given:**

At time

**Formula used:**

The general logistic equation is

**Calculation:**

Consider the expression:

Given that at

Further simplify,

Also, given that at

**(b)**

To determine

**To calculate:** The culture weight after 5 years.

**(c)**

To determine

**To calculate:** The time when the weight will reach 18 g.

**(d)**

To determine

**To calculate:** The logistic differential equation that models growth rate of the culture’s weight. Also, use Euler’s method with step size of

**(e)**

To determine

**To calculate:** The hours after which the culture’s weight is increasing most rapidly.

Calculus: Early Transcendental Functions (MindTap Course List)

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The populations of two species...Ch. 6.6 - Revising the Predator-Prey Equations Consider a...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General SolutionIn Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General Solution In Exercises 3-8, 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...Ch. 6 - Solving a Differential Equation In Exercises...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...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Finding an Exponential Function In Exercises...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 InterestFine the balance in an account...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Sales The sales 5 (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 43 and 44, sketch a few...Ch. 6 - Slope Field In Exercises 43 and 44, sketch a few...Ch. 6 - Using a Logistic Equation In Exercises 49 and 50,...Ch. 6 - Using a Logistic Equation In Exercises 49 and 50,...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 - Sales Growth The rate of change in sales 5 (in...Ch. 6 - Sales Growth Use the result of Exercise 55 to...Ch. 6 - Learning Theory In Exercises 57 and 58, assume...Ch. 6 - Learning Theory In Exercises 57 and 58, assume...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...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Writing In Exercises 6769. write an example of the...Ch. 6 - Writing In Exercise 6769. write an example of the...Ch. 6 - Writing In Exercises 6769, write an example of the...Ch. 6 - Investment Let A(t) be the amount in a fund...Ch. 6 - Investment A retired couple plans to withdraw P...Ch. 6 - Investment Use the result of Exercise 70 to find...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Doomsday Equation The differential equation where...Ch. 6 - Sales Let S represent sales of a new product (in...Ch. 6 - Error Using the Product Rule Although it is true...Ch. 6 - Torricellis 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 - Finding a Function Consider a function f such that...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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