(a) Show that if P satisfies the logistic equation (1), then (b) Deduce that a population grows...

Question:

(a) Show that if P satisfies the logistic equation (1), then

(b) Deduce that a population grows fastest when it reaches half its carrying capacity.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

See More Books

Question Posted: Jul 07, 2010 04:25 AM

See More Questions

(a) Show that if P satisfies the logistic equation (4), then (b) Deduce that a population grows fastest when it reaches half its carrying capacity. 2P d?P k*P = kP[ 1 dt?
Show that if p and q are distinct prime numbers, then pq1 + qp1 1 (mod pq).
Show that if p is an nth-degree polynomial, then N7 p(x + 1) = 2"(x).
A simple beam AB of span length L = 24ft is subjected to two wheel loads acting at distance = 5 ft apart (see figure). Each wheel transmits a load P = 3.0 k, and the carriage may occupy any position...
According to the U.S. Census Bureau, 7.1% of all babies born are of low birth weight ( <5 lb, 8 oz). An obstetrician wanted to know whether mothers between the ages of 35 and 39 years give birth to a...
As an alternative method of evaluating a group home, suppose we take 12 adolescents who have been declared delinquent. We take the number of days truant during each of three time periods: (1) the...
Chase Publishing Company purchased the copyright to a financial textbook for $\$ 25,000$. Although the author thought the book would serve academia for 10 years, the reality is that the typical life...
Twelve tasks, with times and precedence requirements as shown in the following table, are to be assigned to workstations using a cycle time of 1.5 minutes. Two heuristic rules will be tried: (1)...
S Tiger Trade has the following cash transactions for the period. Accounts Cash received from sale of products to customers Cash received from the Bank for long-term loan Cash paid to purchase...
Presented below are selected transactions at Metlock, Inc. for 2020. Jan. 1 Retired a piece of machinery that was purchased on January 1, 2010. The machine cost $61,800 on that date. It had a useful...
Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 10,000. The number of fish tripled in the first...
For a fixed value of k (say k = 10), the family of logistic functions given by Equation 4 depends on the initial value P0 and the proportionality constant k. Graph several members of this family. How...
Solve the given systems of equations by using the inverse of the coefficient matrix. 2.5x + 2.8y = 3.0 3.5x 1.6y= 9.6
Would you advise corporations to set a goal of becoming debt-free? Would you advise young people to set becoming debt-free as a goal? Explain. At what age would you like to become debt-free, i.e.,...
Mr. X wishes to buy a machine after 3 years. He plans to deposit Ksh. 20,000 at the end of each year into a bank savings account paying a fixed rate of interest of 7 % for the same. What is its...
How do investors use stock fundamentals to construct portfolios? Please use any three fundamentals to illustrate the method.
According to https://www.youtube.com/watch?v=zWhYXYrK1BI, examine dollar index strategy based on SPY monthly returns from Jan. 2000 through Jan. 2022. Does the strategy outperform buy-and-hold...
6. Payments of 300, 500 and 700 are made at the end of years five, six and eight, respectively. Interest is accumulated at an annual effective rate of 4%. You are to find the point in time at which a...
Two-tailed test with $\alpha=0.10$, degrees of freedom in the numerator $=12$, degrees of freedom in the denominator $=20$. Find the critical value( $s$ ) for $\alpha$.
A circular concrete shaft liner with Youngs modulus of 3.4 million psi, Poissons ratio of 0.25, unconfined compressive strength 3,500 psi and tensile strength 350 psi is loaded to the verge of...
What volume does 300 g of mercury occupy? The density of mercury is 13 600.
The Power of Trade and Comparative Advantage: Work It Out 3 ? Here's another specialization and exchange problem. This problem is wholly made-up, ? so that you won't be able to use your intuition...
Government spending as a fiscal policy tool is used to: A) ?Decrease the national debt B) ?Directly stimulate economic activity by increasing demand C) ?Reduce inflation D) ?Lower interest rates
Automobile demand has fallen during a recent recession, and Ana has been laid off from her job on the assembly line. Rajiv recently lost his job as a waiter at a local restaurant. A recent increase...

(a) Show that if P satisfies the logistic equation (1), then (b) Deduce that a population grows...

Question:

2P d*P dr? K

Step by Step Answer:

dP 2 KP12 dt P dP dP dP KP P 1 k dt dt K dt ...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions