Exponential Growth and Decay. Linear GrowthExponential Growth Page 5.

Slides:

Advertisements

Similar presentations

Exponential Functions

Advertisements

Linear vs. exponential growth Linear vs. exponential growth: t = 0 A = 1x(1+1) 0 = 1 A = 1x0 + 1 = 1.

Warm-Up Identify each variable as the dependent variable or the independent for each of the following pairs of items the circumference of a circle.

Rational Numbers and Decimals

NO CALCULATORS!!!!!!!.  Integers are the whole numbers and their opposites (no decimal values!)  Example: -3 is an integer  Example: 4 is an integer.

5.3 Solving Systems using Elimination

Partner practice Chapter 8 Review WHITEBOA RD. Chapter 8 Review DRAW -The basic shape of the graph of a linear equation -The basic shape of the graph.

Lesson 3.8 Solving Problems Involving Exponential Functions

Solving Linear Equations

7-6 & 7-7 Exponential Functions

Algebra 1 Warm Up 9 April 2012 State the recursive sequence (start?, how is it changing?), then find the next 3 terms. Also find the EQUATION for each.

Do Now Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?

The Natural Base e Section 6.2 beginning on page 304.

Unit 7: Non-Linear Equations & Real- World Applications Section 1: Compound Interest Using 5x³: 5 is the coefficient, x is the base, 3 is the exponent.

Chapter 8 Exponents and Exponential Functions

Exponential Growth Exponential Decay Graph the exponential function given by Example Graph the exponential function given by Solution x y, or f(x)

Imagine this much bacteria in a Petri dish Now this amount of the same bacteria Assuming that each bacterium would reproduce at the same rate, which dish.

Exponential Growth & Decay

8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.

7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.

Essential Question: How do you find a growth factor and a decay factor?

Unit 1: Integers.  Subtracting Integers can be tough; however, the trick is to make the subtraction problem into an addition problem! = ______Can.

Exponential Growth and Decay

Learning about Using Inverse Operations for finding the original price after a percentage increase or decrease.

 Solve one of the equations for one of the variables.  Isolate one of the variables in one of the equations.  Choose whichever seems easiest.  Substitute.

Exponential Functions Exponential Growth Exponential Decay Created by: David W. Cummins.

Exponential Functions y = a(b) x Exponential Growth This graph shows exponential growth since the graph is increasing as it goes from left to right.

7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.

Exponential Growth & Decay

Positive and Negative numbers. Negative numbers A positive or negative whole number, including zero, is called an integer. For example, –3 is an integer.

9.1 Exponential Functions

Review of Chapter 8. Graphing Exponential Functions: Make and table and graph the function for the domain {0, 1, 2, 3} Plug in 0, 1, 2, and 3 in for x.

Growth and Decay: Integral Exponents

Section 3.1 Exponential Functions. Upon receiving a new job, you are offered a base salary of $50,000 plus a guaranteed raise of 5% for each year you.

Essential Skills: Solve problems involving exponential growth Solve problems involving exponential decay.

GrowthDecay. If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by.

Exponential Growth and Decay 6.4. Slide 6- 2 Quick Review.

Scientific Notation.  Allows us to write very big and very small numbers.

Scientific Notation. Scientific (Exponential) Notation A number is written as the product of two numbers, a coefficient and 10 raised to a power 36,000.

UNIT 3: EXPONENTS, RADICALS, AND EXPONENTIAL EQUATIONS Final Exam Review.

Exponential Growth and Decay. Exponential Growth When you have exponential growth, the numbers are getting large very quickly. The “b” in your exponential.

Lesson 7.1 Lesson 7.2 Lesson 7.4 Lesson A 10 A 15 A 20 A 5 B 10 B 15 B 20 B 5 C 10 C 15 C 20 C 5 D 10 D 15 D 20 D 10 E 15 E 20 E 25 E 10 F 15 F.

Exponential Growth Exponential Decay Example 1 Graph the exponential function given by Solution xy or f(x) 0 1 –1 2 – /3 9 1/9 27.

8-2: Exponential Decay Day 2 Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.

8.1 & 8.2 Exponential Functions 3/10/2014. In this lesson we will learn … What an exponential function is. Difference between exponential growth and decay.

7.4 Subtracting Linear Expressions. Distributing the Negative If there is a negative sign on the out side of the parenthesis add a 1 to it and distribute.

Solve Linear Systems by Elimination February 3, 2014 Pages

Family of Functions, review Which functions are nonlinear? Select all that apply.

8.2 Interest Equations Key Q-How is an exponential function used to find interest? These are all money problems so you should have two decimal places.

Exponential Decay –Modeled with the function: y = a b x for a > 0 and 0 < b < 1. y = a b x a = the starting amount (when x = 0) b = the base, which is.

Scientific Notation SWBAT write the scientific notation for numbers given in standard form; write the standard form for numbers given in scientific notation;

Non-Linear Functions and Real-World Applications.

Scientific Notation. What is Scientific Notation? Scientific notation is a way of writing extremely large or small measurements. The number is written.

10.2 Exponential and Logarithmic Functions. Exponential Functions These functions model rapid growth or decay: # of users on the Internet 16 million (1995)

If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the equation.

6.4 Exponential Growth and Decay Greg Kelly, Hanford High School, Richland, Washington Glacier National Park, Montana Photo by Vickie Kelly, 2004.

Exponential Growth and Decay

13 – Exponential vs. Linear Functions Calculator Required

Applications of Exponential Functions

7. The tuition at a private college can be modeled by the equation ,

E-4. 4: Constant Ratios in the context of Real-world Situations E-4

Linear Equations Y X y = x + 2 X Y Y = 0 Y =1 Y = 2 Y = 3 Y = (0) + 2 Y = 2 1 Y = (1) + 2 Y = 3 2 Y = (2) + 2 Y = 4 X.

Warm Up Find a partner at your table.

Objective - To add and subtract decimals.

17 – Exponential Modeling – Creating an Equation Calculator Required

Good Morning ! Here’s your warm up..

Addition & Subtraction Addition & Subtraction

X ⦁ X = 64 ±8 ±14 X ⦁ X ⦁ X =

Presentation transcript:

Exponential Growth and Decay

Linear GrowthExponential Growth Page 5

Page 6

Page 8

Annual Growth vs. Continuous Growth: Annual Growth: The +/- means you either add or subtract the rate depending upon the problem. Are you earning money or losing money? Page 11

Here are the answers to the last two questions: This equation was an increasing problem. Notice that the number in the ( ) is greater than one! This equation was a decreasing problem. Notice that the number in the ( ) is less than one! Keep this in mind when doing annual growth problems! Page 11

Page 12

Before we do continuous growth, we need to look at the natural number “e”. This is very similar to the other exponential functions. “e” is called the natural number and is used to do continuous growth!

Annual Growth vs. Continuous Growth: Continuous Growth: When we write the rate, we still need to change it to a decimal. If it is an increasing problem, we write the rate as a positive number. If it is a decreasing problem, then you write the rate as a negative number Since this is an increasing problem, the rate is written as a positive. Page 11

Since this is a decreasing problem, the rate is written as a negative.

Page 12