Write a differential equation to represent this. Key word RATE

Slides:



Advertisements
Similar presentations
Diff EQs 6.6. Common Problems: Exponential Growth and Decay Compound Interest Radiation and half-life Newton’s law of cooling Other fun topics.
Advertisements

Functions of Several Variables. Constructing Functions of Several Variables The temperature at points in the xy-plane is proportional to the square of.
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Exponential Growth and Decay Section 6.4.
Differential Equations and Linear Algebra Math 2250
Exponential Growth and Decay Newton’s Law Logistic Growth and Decay
Functions of two variables Graphical, Numerical and Analytical Points of view.
Differential Equations as Mathematical Models. Population Dynamics Animal Population The number of field mice in a certain pasture is given by the function.
Reaction Rates. Chemical Equation Review Chemical Reactions Every reaction has a chemical equation. The reaction of nitrogen monoxide with ozone produces.
Sullivan PreCalculus Section 4
Section 1.2 Some Mathematical Models. TERMINOLOGY A model starts by (i) identifying the variables that are responsible for changing the system and (ii)
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.
Applications Differential Equations. Writing Equations.
Logarithmic Functions. Example1. On the Richter Scale, the magnitude R of an earthquake of intensity I is given by where I 0 is a certain minimum intensity.
Differential Equations Copyright © Cengage Learning. All rights reserved.
College and Engineering Physics Newton’s Laws 1 TOC First Law - Inertia Second Law – Force and Acceleration Third Law – Action and Reaction Introduction.
Unit 9 Exponential Functions, Differential Equations and L’Hopital’s Rule.
Differential Equations
9.4 Exponential Growth & Decay
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.
Direct Variation  Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number.
Do Now: Use the differentiation rules to find each integration rule. Introduction to Integration: The Antiderivative.
Inverse Trig Functions and Standard Integrals
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.
SOLVING PERCENTAGE of CHANGE EQUATIONS PRE213 A dress costs $45 but there’s a 25% off sale. What’s the new price? Sometimes it helps to use a table to.
Warm Up Dec. 19 Write and solve the differential equation that models the verbal statement. Evaluate the solution at the specified value. The rate of change.
Aim: Growth & Decay Course: Calculus Do Now: Aim: How do we solve differential equations dealing with Growth and Decay Find.
Def: The mathematical description of a system or a phenomenon is called a mathematical model.
Ch. 7 – Differential Equations and Mathematical Modeling 7.4 Solving Differential Equations.
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.
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
7-4 Exponential Growth and Decay
Newton’s Law of Cooling
6.4 Growth and Decay.
Newton's Law of Cooling and other applications of differential equations Section 5-M.
Drill.
3.1 Growth and Decay.
Exponential Growth and Decay
Differentiation and integration part 1
What would the next picture in the pattern look like?
6.2 Exponential Growth and Decay
What do all of these have to do with Calculus?!?!?
Calculus II (MAT 146) Dr. Day Friday, March 23, 2018
Differentiation.
Differential Equations Growth and Decay
6.4 day 2 Exponential Growth and Decay
Differentiation.
Integration 2 and Differential equations
Newton’s Law of Cooling
Differential Equations
6.4 Applications of Differential Equations
Specialist Mathematics
7.6 - Laws of Growth and Decay
7.4 Exponential Growth and Decay Glacier National Park, Montana
Section 4.8: Exponential Growth & Decay
Exponential Growth and Decay
Calculus II (MAT 146) Dr. Day Wednesday, March 28, 2018
Section 4.8: Exponential Growth & Decay
Precalculus Essentials
3.8 Exponential Growth and Decay
Which equation does the function {image} satisfy ?
Newton’s Law of Cooling
Kinetic Theory of Gases
Packet #16 Modeling with Exponential Functions
The Combined Gas Law and Avogadro’s Principle
6.2 Differential Equations: Growth and Decay (Part 2)
Differential Equations As Mathematical Models
Presentation transcript:

Write a differential equation to represent this. Key word RATE Write a differential equation to represent this. Key word RATE. Support- d…./dt = ……….. Fill in the blanks. These slides create great discussion points and introduce rates of change painlessly! Challenge by asking how height varies with time.

Write a differential equation to represent this.

Write a differential equation to represent this.

Write a differential equation to represent this. Key word PROPORTIONAL Write a differential equation to represent this. Key word PROPORTIONAL. They will need to think back to GCSE.

Write a differential equation to represent this. Speed = rate of change.

The rate at which a particle decays is proportional to the number of particles. Write a differential equation to represent this.

A population is growing at a rate which is proportional to the size of the population. Write a differential equation to represent this.

Newton’s Law of Cooling The rate of loss of temperature of a body is proportional to the excess temperature of the body over its surroundings Write a differential equation to represent this.

Find the volume and surface area

Find the volume and surface area

Find the volume and surface area

Find the volume and surface area

Make up a question to go with this picture

Make up a question to go with this picture

Make up your own rate questions and illustrate them.