Some Applications Involving Separable Differential Equations.

Slides:

Advertisements

Similar presentations

“Teach A Level Maths” Vol. 2: A2 Core Modules

Advertisements

6.2 Growth and Decay Law of Exponential Growth and Decay C = initial value k = constant of proportionality if k > 0, exponential growth occurs if k < 0,

CHAPTER Continuity Exponential Growth and Decay Law of Natural Growth(k>0) & (Law of natural decay (k

Copyright © Cengage Learning. All rights reserved.

ACTIVITY 40 Modeling with Exponential (Section 5.5, pp ) and Logarithmic Functions.

7 INVERSE FUNCTIONS. 7.5 Exponential Growth and Decay In this section, we will: Use differentiation to solve real-life problems involving exponentially.

Differential Equations

Exponential Growth and Decay

Clicker Question 1 The radius of a circle is growing at a constant rate of 2 inches/sec. How fast is the area of the circle growing when the radius is.

7.6 Differential Equations. Differential Equations Definition A differential equation is an equation involving derivatives of an unknown function and.

4.5 Modeling with Exponential and Logarithmic Functions.

Copyright © Cengage Learning. All rights reserved.

Differential Equations and Linear Algebra Math 2250

Applications of Linear Equations

9.3 Separable Equations.

Exponential Growth and Decay February 28, P 404 Problem 5 The population of a colony of mosquitoes obeys the law of uninhibited growth. If there.

Warmup 1) 2). 6.4: Exponential Growth and Decay The number of bighorn sheep in a population increases at a rate that is proportional to the number of.

College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.

Exponential Growth and Decay 6.4. Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that.

4.8 Exponential and Logarithmic Models

1 SS Solving Exponential Equations MCR3U - Santowski.

Chapter 1: First-Order Differential Equations 1. Sec 1.4: Separable Equations and Applications Definition A 1 st order De of the form is said to.

L’Hospital’s Rule: f and g – differentiable, g(a)  0 near a (except possibly at a). If (indeterminate form of type ) or (indeterminate form of type )

Section 7.4: Exponential Growth and Decay Practice HW from Stewart Textbook (not to hand in) p. 532 # 1-17 odd.

Chapter 3 – Differentiation Rules

Using calculus, it can be shown that when the rate of growth or decay of some quantity at a given instant is proportional to the amount present at that.

Sec 1.3 Differential Equations as Mathematical Models Sec 3.1 Linear Model.

Copyright © Cengage Learning. All rights reserved. 9 Differential Equations.

EXPONENTIAL GROWTH & DECAY; Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential.

Differential Equations

9.4 Exponential Growth & Decay

AP CALCULUS AB Chapter 6:

7.4 B – Applying calculus to Exponentials. Big Idea This section does not actually require calculus. You will learn a couple of formulas to model exponential.

MTH 253 Calculus (Other Topics)

Section 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models.

Wednesday, Oct 21, 2015MAT 146. Wednesday, Oct 21, 2015MAT 146.

Exponential Growth and Decay; Newton’s Law; Logistic Models

Any population of living creatures increases at a rate that is proportional to the number present (at least for a while). Other things that increase or.

7.3B Applications of Solving Exponential Equations

6.7 Growth and Decay. Uninhibited Growth of Cells.

Aim: Growth & Decay Course: Calculus Do Now: Aim: How do we solve differential equations dealing with Growth and Decay Find.

3.8 - Exponential Growth and Decay. Examples Population Growth Economics / Finance Radioactive Decay Chemical Reactions Temperature (Newton’s Law of Cooling)

6.4 Exponential Growth and Decay Objective: SWBAT solve problems involving exponential growth and decay in a variety of applications.

MAT 1235 Calculus II Section 9.3 Separable Equations II Version 2

6.4 Exponential Growth and Decay. The number of bighorn sheep in a population increases at a rate that is proportional to the number of sheep present.

6.4 Applications of Differential Equations. I. Exponential Growth and Decay A.) Law of Exponential Change - Any situation where a quantity (y) whose rate.

Differential Equations MTH 242 Lecture # 07 Dr. Manshoor Ahmed.

Salt Questions.

6.4 Exponential Growth and Decay Law of Exponential Change Continuously Compounded Interest Radioactivity Newton’s Law of Cooling Resistance Proportional.

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

9/27/2016Calculus - Santowski1 Lesson 56 – Separable Differential Equations Calculus - Santowski.

Seating by Group Thursday, Oct 27, 2016 MAT 146.

Seating by Group Friday, Oct 28, 2016 MAT 146.

Differential Equations

Seating by Group Thursday, Nov 3, 2016 MAT 146.

Warm-up Problems Solve the homogeneous DE Solve the Bernoulli equation.

Differential Equations

Exponential Growth and Decay

6.4 Exponential Growth and Decay, p. 350

Setting up and Solving Differential Equations

7.4 Exponential Growth and Decay

Lesson 58 - Applications of DE

Section 10.1 Separable Equations II

6.4 Applications of Differential Equations

Copyright © Cengage Learning. All rights reserved.

7.6 - Laws of Growth and Decay

9.1/9.3 – Differential Equations

Chapter 5 APPLICATIONS OF ODE.

Laws of Growth and Decay!!!

Chemical Engineering Mathematics 1. Presentation Contents Chemical Engineering Mathematics2  Partial Differentiation Equation in long non-uniform rod.

Presentation transcript:

Some Applications Involving Separable Differential Equations

Mixing Problem A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L / min. The solution is kept thoroughly mixed and drains from the tank at the same rate. Find a formula for the amount of salt in the tank at any time t. How much salt remains in the tank after ½ hour?

Bacterial Growth A common inhabitant of the human intestines is the bacterium Escherichia Coli. A cell of this bacterium in a nutrient broth medium divides into two cells every 20 minutes. The initial population of a culture is 60 cells. (A) Find the relative growth rate of E. Coli. (B) Find an expression for the number of cells after t hours. (C) Find the number of cells after 8 hours and find the growth rate of the culture after 8 hours. (D) When will the population of the culture reach 20,000 cells?

Chemical Reactions In an elementary chemical reaction, single molecules of two reactants, X and Y, form a molecule of the product Z. The Law of Mass Action states that the rate of the reaction is proportional to the product of the concentrations of X and Y. Assuming that the initial concentration of X is x(0)=a moles/L, the initial concentration of Y is y(0)=b moles/L, and the initial concentration of Z is z(0)=0 moles/L, find a formula for the function z(t) (which is the concentration of the product at any time t). To do this, consider two cases: the case that a and b are different and the case that a and b are the same. C

Radioactive Decay The half-life of radium-226 is 1590 years. (A)A sample of radium-226 has a mass of 100 mg. Find a formula for the mass of radium-226 that remains after t years. (B)Find the mass after 1000 years. (C)When will the mass be reduced to 30 mg?

Newton’s Law of Cooling A thermometer is taken from a room where the temperature is 20 0 C to the outdoors where the temperature is 5 0 C. After one minute, the temperature reads 12 0 C. (A)What will the reading on the thermometer be after one more minute? (B)At what time will the thermometer read 6 0 C?