In the study of population dynamics one of the most famous models for a growing but bounded

Question:

In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation

dP/dt = P(a - bP),

where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course in Differential Equations with Modeling Applications

ISBN: 978-1305965720

11th edition

Authors: Dennis G. Zill

See More Books

Question Posted: Jul 09, 2018 02:09 PM

See More Questions

One widely used nonlinear model of competition is the logistic model, where per capita production is a linearly decreasing function of population size. Suppose that per capita production has a...
The following system of differential equations is encountered in the study of the decay of a special type of radioactive series of elements: dx/dt = 1 x dy/dt = 1 x 2 y, where 1 and 2 are...
In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern...
Adam Kleen Enterprise (AKE) was initially set up as a convenient shop selling laundry related items by Adam Bollan. Despite having good results in the national-level examination and was even offered...
Andrew Peller Limited and Magnotta Winery Corporation are two producers of quality wines in Canada. Selected financial data (in thousands) for these two competitors for a recent year are as follows:...
Use the option data from July 13, 2009 in the following table to determine the rate Google would have paid if it had issued $128 billion in zero-coupon debt due in January 2011. Suppose Google...
In Figure P8.35, a $55-\mathrm{kg}$ skier heads down a slope, reaching a speed of $27 \mathrm{~km} / \mathrm{h}$. They then slide across a horizontal snow field but hit a rough area. Assume the...
Updike Upholstery cuts and sews fabric for custom ordered chairs, ottomans, and sofas. Often, the more complicated patterns are for the smaller pieces, where cutting is more time consuming than...
15. If y = 3x-4x+2 then slope at x = 1 is: (1) 1 (2) 2 (3) 4 (4) -2 16. sin240 = ? (1) - 2 (3) 3 1/2 17. Value of sin 2 is (4) (2) 12 (1) 23 (2) (3) 90 180 (4) 0 18. The rate of mass of the gas...
Several years after reengineering its production process, Dettling Corporation hired a new controller, Alana Metzgar. She developed an ABC system very similar to the one used by Dettling's chief...
Use Eulers method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) by hand, first using h = 0.1 and then using h = 0.05. y' = 2x - 3y + 1, y(1) = 5; y(1.2)
We saw that a mathematical model for the velocity v of a chain slipping off the edge of a high horizontal platform is xv dv/dx + v 2 = 32x. In that problem you were asked to solve the DE by...
How does the comparative-cost concept relate to a nations production possibilities schedule? Illustrate how differently shaped production possibilities schedules give rise to different opportunity...
Rania Corporation manufactured 100,000 buckets during February. The overhead cost-allocation base is $5.00 per machine-hour. The following variable overhead data pertain to February: Requirements 1....
Briefly explain financial perspectives in a balanced scorecard.
Knots and Reynolds provides hair-cutting services in the local community. In February, the business cut the hair of 240 clients, earned $4,900 in revenues, and incurred the following operating costs:...
As part of the restructuring exercise in your galvanized tin firm, you have been assigned to the marketing division where your role will be to advise on the pricing and costing of the firms two new...
Yem Company manufactures luggage sets. Yem sells its luggage sets to department stores. Yem expects to sell 2,050 luggage sets for $320 each in January and 2,200 luggage sets for $320 each in...
An industrial machine costing $14,000 will produce net cash savings of $5,000 per year. The machine has a five-year useful life but must be returned to the factory for major repairs after three years...
Planning: Creating an Audience Profile; Collaboration: Team Projects. Compare the Facebook pages of three companies in the same industry. Analyze the content on all available tabs. What can you...
In problem use the procedures developed in this chapter to find the general solution of each differential equation. y'' - 2y' + 2y = e x tan x
In problem use the procedures developed in this chapter to find the general solution of each differential equation. y'' y = 2e x /e x + e -x
In problem use the procedures developed in this chapter to find the general solution of each differential equation. 6x 2 y'' + 5xy' - y = 0
The following trial balance was drawn from the records of Zachary Company as of October 1, year 2. Cash Accounts receivable Inventory Store equipment Accumulated depreciation Accounts payable Line of...
Calculate the number of units sold and units remaining in ending inventory. Book "rint erences Check my wa Car Armour sells car wash cleaners. Car Armour uses a perpetual inventory system and made...
Eliminating Entries, Goodwill Pendragon Corporation acquired all of the stock of Sherwood, Inc. for $500 million in cash. Sherwood's shareholders' equity accounts at the date of acquisition were as...

In the study of population dynamics one of the most famous models for a growing but bounded

Question:

Step by Step Answer:

Write the differential equation as dPdt aP bP 2 and let u P 1 or P u 1 Then ...View the full answer

A First Course in Differential Equations with Modeling Applications

Students also viewed these Mathematics questions