7. A population is modeled by a function y(t) that satisfies the logistic differential equation= 2y(1 – ).dydtA. What is lim y(t)? Explain.B. For what value of y is the population growing the fastest?C. Find the particular solution satisfying y(0) = 3.

We have to evaluate limt→∞ yt for the first-order differential equation dydt=2y1-y5. We can write it…

Answered: 7. A population is modeled by a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

4. The equation of motion of a particle is s(t) = e' (t² – 3), where s is in meters and t is in seconds with t2 0. (a) Find the velocity, v(t), of the particle using the product rule and simplify. (b) Find v(1) and explain what this means in terms of the movement of the particle. (c) Find the acceleration function, a(t), and calculate the value of a(0) and explain what it means.
o H.W 2- Mathemati... > Mathematics I / H.W2 / -3-a (2020-2021) Q1 / Find dy/dx by using the definition of derivatives for the following functions; 1. y = 2. f(x) = x³ 3. f(x) = x² – 5x + 9 4. f(x) = 1/x² Q2 / Find dy/dx for the following functions; 1. y = Vtan(sin(x² – 1)) 2.습(1+ cot x)3) 3. Q3 / Find d²y/dx² for the following; 1.Gsec 3:) 2. x = t - t3, y = 2t + 5 Q4 / Find the angle between the curves x² = y & y? = x Q5 / Sketch the graph of function %=+ 3x y = II
2. (Separable and Newton's Law of Cooling) Let T(t) be the temperature of the room and T, the outside temperature (assumed to be constant in Newton's law). Then by Newton's law dt k(T – T,). In this problem, the rate at which a substance cools in air is directly proportional to the difference between the temperatures of the substance and that of air. The temperature of air, TA, is 30° and the substance cools from 100° to 70° in 15 minutes. How long does it take for the substance to cool from 100 to 50"? A. 45.30 minutes B. 43.60 minutes C. 35.39 minutes D. 33.59 minutes Solution. Hints: 1. Find the general solution of the equation = k(T – T,) by separable. 2. Let t = 0 and T = 100° to find C. 3. Let t = 15 and T = 70 to find k. 4. Let T = 50° to find t.
C,d,e
1.Find the derivative of the function. y=2x−5/7x+3 The solution is y′=nothing.
2.[15] The acceleration of an object is given by the equation a = t + 4 (m/s²). The object has an initial velocity of 5 m/s. How far has the object traveled after 10 seconds?
17. If P'(t) is the rate a deer population grows per year, write a sentence explaining what P'(t) dt represents. 18. v(t) = t - 3 is the velocity of a particle in cm/sec. Find the distance traveled by the particle in the first four seconds.
LEM 1: Determine the number of derivatives required for the functions to be equal to zero. y(t) = t²-t + 15 y = (x² - 1)³
b) The general form of Newton's Law of cooling is: T(t) = Ta + (T(0) - Ta)e-kt where I is the temperature at any time, t. Ta is the surrounding ambient temperature and k is the cooling constant. Consider a cup of coffee at an initial temperature, T(0) of 80°C placed into the open air at 15°C. After 5 minutes the coffee cools to 65°C. Using these initial conditions: i) Calculate the cooling constant, k ii) How long will it take for the coffee to reach 20°C?
1. A particle moves along a vertical coordinate axis so that its position at any time t20 is given by the function s() =r' - 6r² + 9t + 5, where s is measured in centimeters and t is measured in seconds. (e) Describe the motion of the particle for t20. Answer the following questions with justification: • When is the particle moving up? • When is the particle moving down?. • When is the particle at rest? • When is the particle speeding up? • When is the particle slowing down? because because because because because • Find the particle's acceleration each time the velocity is zero. • Find the total distance traveled by the particle from 0 to 3 seconds.
4.3 2
Find the first derivative of the function of f(x) using any method?

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

7. A population is modeled by a function y(t) that satis fies the logistic differential equation dy = 2y(1 - 공). dt A. What is lim y(t)? Explain. B. For what value of y is the population growing the fastest? C. Find the particular solution satisfying y(0) = 3.