Explanation Given: The differential Gompertz equation. is M ′ ( t ) = − r M ln ( M K ) with its initial point M ( 0 ) = M 0 and the value of r = 0.6 , K = 5500 and M 0 = 20 . Calculation: The differential Gompertz equation is M ′ ( t ) = − r M ln ( M K ) . The values are r = 0.6 , K = 5500 and M 0 = 20 . That means, the Gompertz equation is M ′ ( t ) = − 0.6 M ln ( M 5500 ) . Rewrite the above differential equation as follows, M ′ ( t ) M ln ( M 5500 ) = − 0.6 Integrate on both sides of the above expression with respect to t as follows, ∫ M ′ ( t ) M ln ( M 5500 ) d t = ∫ − 0.6 d t To solve the above integral, consider the following assumption. That is, Take ln ( M 500 ) = z Then, d ln ( M 5500 ) d t = d z d t 5500 M × d ( M 5500 ) d t = d z d t 5500 M × 1 5500 × d M d t = d z d t ( M ′ ( t ) M ) d t = d z Substitute these values in above integration ∫ M ′ ( t ) M ln ( M 5500 ) d t = ∫ − 0.6 d t . That is, ∫ d z z = ∫ − 0.6 d t ln z = − 0.6 t + C Substitute the value of z = ln ( M 5500 ) in the above solution. ln | ln ( M 5500 ) | = − 0.6 t + C Where C is constant. Take exponential on both sides of the above solution as follows, e ln | ln ( M 5500 ) | = e − 0

Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package

3rd Edition

ISBN: 9780136207764

Author: Briggs, William, Cochran, Lyle, Gillett, Bernard, SCHULZ, Eric

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 9.5, Problem 22E

To determine

To solve: The Gompertz equation for the given value and graph its solution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 21E

Chapter 9.5, Problem 23E

Students have asked these similar questions

u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

K Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. x-7 p(x) = X-7 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = OB. f is discontinuous at the single value x= OC. f is discontinuous at the two values x = OD. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - ∞. The limit for the smaller value is The limit for the larger value is The limit for the smaller value is The limit for the larger value does not exist and is not c∞ or -

Chapter 9 Solutions

Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - What is the solution of the initial value problem...Ch. 9.1 - Solve the initial value problem in Example 4a with...Ch. 9.1 - Suppose the initial conditions in Example 5a are...Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Consider the differential equation y(t) + 9y(t) =...Ch. 9.1 - If the general solution of a differential equation...Ch. 9.1 - Does the function y(t) = 2t satisfy the...Ch. 9.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. 9.1 - The solution to the initial value problem y(t) = 2...

Additional Math Textbook Solutions

Find more solutions based on key concepts

Find how many SDs above the mean price would be predicted to cost.

Intro Stats, Books a la Carte Edition (5th Edition)

4. You construct a 95% confidence interval for a population mean using a random sample. The confidence interval...

Elementary Statistics: Picturing the World (7th Edition)

Sampling Method. In Exercises 9–12, determine whether the sampling method appears to be sound or is flawed. 9. ...

Elementary Statistics (13th Edition)

CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...

Thinking Mathematically (6th Edition)

1. How many solutions are there to ax + b = 0 with ?

College Algebra with Modeling & Visualization (5th Edition)

Fill in each blank so that the resulting statement is true. Any set of ordered pairs is called a/an ____.The se...

Algebra and Trigonometry (6th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The Gompertz equation for the given value and graph its solution.

Solution Summary: The author explains how to solve the Gompertz equation for the given value and graph its solution.