User Account

All Pages

Write and solve the logistic differential equation modeling

Assignment Help Mathematics
Reference no: EM131612726

Question: Use the logistic function obtained in Problem to model the growth of P, the total oil produced worldwide in billions of barrels since 1859:

(a) Find the projected value of P for 2010.

(b) Estimate the annual world oil production during 2010.

(c) How much oil is projected to remain in the ground in 2010?

(d) Compare the projected production in part (b) with the actual figure of 26.9 billion barrels.

Problem: We define P to be the total oil production worldwide since 1859 in billions of barrels. In 1993, annual world oil production was 22.0 billion barrels and the total production was P = 724 billion barrels. In 2008, annual production was 26.9 billion barrels and the total production was P = 1100 billion barrels. Let t be time in years since 1993.

(a) Estimate the rate of production, dP/dt, for 1993 and 2008.

(b) Estimate the relative growth rate, (1/P)(dP/dt), for 1993 and 2008.

(c) Find an equation for the relative growth rate, (1/P)(dP/dt), as a function of P, assuming that the function is linear.

(d) Assuming that P increases logistically and that all oil in the ground will ultimately be extracted, estimate the world oil reserves in 1859 to the nearest billion barrels.

(e) Write and solve the logistic differential equation modeling P.

Reference no: EM131612726

Questions Cloud

Competitive forces confronting under armour : How strong are the competitive forces confronting Under Armour, Nike, and The Adidas Group? Provide a five-forces analysis to support your answer.
Discuss death penalty should be applied for everyone : The court enforcement as state and federal have the responsibility to process the death penalty base on how the constitutional's Bill of Rights is supported
Explain effective rhetorical strategies used by the author : Your essay will identify and explain effective rhetorical strategies used by the author, Aristotelian appeals generated by these rhetorical strategies.
Investment in a knowledge management project : How might you attempt to justify investment in a knowledge management project?
Write and solve the logistic differential equation modeling : Compare the projected production in part (b) with the actual figure of 26.9 billion barrels.
Signal to the entrepreneur : Explain how profit works as a signal to the entrepreneur.
Discuss the capital budgeting model : Describe the implications of a positive, negative, and zero NPV - Discuss the capital budgeting model, including the process
Define the supply reduction strategy of drug enforcement : What are the four different tactics used in the supply reduction strategy of drug enforcement. Use examples to illustrate
Importance of integrating sales and operations : In this lesson, we discuss the importance of integrating sales and operations. This idea of integrated management is indeed a key tenet of supply chain.

Reviews

Write a Review

Mathematics Questions & Answers

  Here is a worker with talent

Here is a worker with talent θ. There is a market of potential employerswho are willing to pay a wage equalling the talent level. The worker knows thetalent, but the employers do not. They believe talent to be normally distributedwith mean μθ and pre..

  Estimate odgi when the ozone hole will have recovered

During the 1970s and 1980s, the build up of chlorofluorocarbons (CFCs) created a hole in the ozone layer over Antarctica.

  Information systems infrastructure of healthcare

The technical report and the nontechnical presentation will identify compromises and vulnerabilities in the information systems infrastructure of the healthcare organization, and identify risks to the organization's data. You will propose a way to..

  Which country has a comparative advantage in producing milk

Suppose that Hereland's citizens would like 1 truckload of milk and 6 tons of corn. Can Hereland produce this?

  Implement the boolean function

implement the following Boolean function F, together with the don't care conditions d, USE NO MORE THAN TWO NOT GATES:

  Difference between entrepreneurs and inventors

What is the difference between entrepreneurs and inventors? What is the difference between entrepreneurs and inventors as defined in entrepreneurship point of view?

  Engineering drop in centre and the mathematics continuous

The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you should consult the textbook, or ask a fellow student, one of the TA's or your professor for help. There are als..

  Probabilities of the markova chain transition probability

Find the classes and the limiting probabilities of the Markova chain transition probability matrix.

  Style effective for conflict resolution

Evaluate the effectiveness of the leadership theory or style, together with the motivational theory, on goal theory. What's the best use of theory for this particular leadership theory or style to motivate employees and achieve goals? Is the leade..

  Calculate the moment of inertia about an axis

A solid disk of radius R is composed of two different materials. For r R=2. Calculate the moment of inertia about an axis through the center and perpendicular to the disk, expressed solely in terms of the total mass M and radius R.

  Find the number of weak compositions

find the number of weak compositions of 25 into five odd partsfind the number of weak compositions of 25 into five odd parts.

  Find the volume of the solid whose base is the region

Find the volume of the solid whose base is the region bounded by y=x^{6}, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +1-415-670-9521

Phone: +1-415-670-9521

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd