Adapted from www.MAthXTC.com. If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and.

Slides:



Advertisements
Similar presentations
E XPONENTIAL G ROWTH M ODEL W RITING E XPONENTIAL G ROWTH M ODELS A quantity is growing exponentially if it increases by the same percent in each time.
Advertisements

Exponential Functions
GrowthDecay. Exponential function – A of the form y=ab x Step 1 – Make a table of values for the function.
6.1 Exponential Growth and Decay Date: ______________.
Exponential Functions
EXPONENTIAL RELATIONS
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.
Lesson 3.9 Word Problems with Exponential Functions
8-8: E XPONENTIAL G ROWTH AND D ECAY Essential Question: Explain the difference between exponential growth and decay.
Students are expected to: Construct and analyse graphs and tables relating two variables. Solve problems using graphing technology. Develop and apply.
Precalc. 2. Simplify 3. Simplify 4. Simplify.
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.
Exploring Exponential Growth and Decay Models Sections 8.1 and 8.2.
Lesson 8.5 and 8.6 Objectives:
Graph Exponential Growth Functions
7-6 & 7-7 Exponential Functions
Exponential Growth & Decay in Real-Life Chapters 8.1 & 8.2.
8-1: Exponential Growth day 2 Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions.
GrowthDecay. 8.2 Exponential Decay Goal 1: I will graph exponential decay functions. Goal 2: I will use exponential decay functions to model real-life.
If a quantity decreases by the same proportion r in each unit of time, then the quantity displays exponential decay and can be modeled by the equation.
Exponential Functions An exponential function is a function of the form the real constant a is called the base, and the independent variable x may assume.
10.7 Exponential Growth and Decay
Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential.
Exponential Functions -An initial amount is repeatedly multiplied by the same positive number Exponential equation – A function of the form y = ab x “a”
8.1 Exponents axax exponent base means a a a … a x times.
Exponential Growth & Decay
7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.
8.1 Multiplication Properties of Exponents Multiplying Monomials and Raising Monomials to Powers Objective: Use properties of exponents to multiply exponential.
8.5 Exponential Growth and 8.6 Exponential Decay FUNctions
Writing Exponential Growth Functions
Review: exponential growth and Decay functions. In this lesson, you will review how to write an exponential growth and decay function modeling a percent.
Exponential Functions Section 5.1. Evaluate the exponential functions Find F(-1) Find H(-2) Find Find F(0) – H(1)
A colony of 10,000 ants can increase by 15%
Exponential Growth & Decay
Objectives:  Understand the exponential growth/decay function family.  Graph exponential growth/decay functions.  Use exponential functions to model.
If a quantity decreases by the same proportion r in each unit of time, then the quantity displays exponential decay and can be modeled by the equation.
Algebra 1 Section 8.5 Apply Exponential Functions When a quantity grows by the same amount each day it is experiencing linear growth. y = mx + b When a.
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 Decay Functions 4.2 (M3) p Warm-Up Evaluate the expression without using a calculator. ANSWER –1 ANSWER –3 2.– ANSWER.
7.1 E XPONENTIAL F UNCTIONS, G ROWTH, AND D ECAY Warm Up Evaluate (1.08) (1 – 0.02) ( ) –10 ≈ ≈ ≈ Write.
Exponential Growth and Decay 6.4. Slide 6- 2 Quick Review.
Algebra 3 Lesson 5.2 A Objective: SSBAT model exponential growth and decay. Standards: C; S.
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 Exponential Growth 8.2 Exponential Decay. Exponential Function An exponential function has a positive base other than 1. The general exponential function.
A PPLICATIONS OF E XPONENTIAL E QUATIONS : C OMPOUND I NTEREST & E XPONENTIAL G ROWTH Math 3 MM3A2.
Exponential Growth and Decay. M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased.
E XPONENTIAL F UNCTIONS GET A GUIDED NOTES SHEET FROM THE FRONT!
Algebra 2 Exploring Exponential Models Lesson 7-1.
Unit 5: Exponential Word Problems – Part 2
10.2 Exponential and Logarithmic Functions. Exponential Functions These functions model rapid growth or decay: # of users on the Internet 16 million (1995)
Drill 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.
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.
E XPONENTIAL W ORD P ROBLEMS Unit 3 Day 5. D O -N OW.
7-7B Exponential Decay Functions Algebra 1. Exponential Decay Where a>0 & 0 < b< 1 a is the initial amount b is the decay factor y-intercept is (0,a)
Exponential Functions
Exponential Growth and Exponential Decay
EXPONENTIAL GROWTH MODEL
6.1 Exponential Growth and Decay Functions
Exponential Functions
Exponential Functions
Exponential Functions
EXPONENTIAL GROWTH MODEL
Exponential Functions
6.1 Exponential Growth and Decay Functions
Notes Over 8.5 Exponential Growth
Exponential Growth and Decay
Exponential Functions
Exponential Functions
Exponential Functions
Presentation transcript:

Adapted from

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 Where C = initial amount r = growth rate (percent written as a decimal) t = time where t  0 (1+r) = growth factor where 1 + r > 1

E XPONENTIAL G ROWTH M ODEL W RITING E XPONENTIAL G ROWTH M ODELS A quantity is growing exponentially if it increases by the same percent in each time period. C is the initial amount. t is the time period. (1 + r) is the growth factor, r is the growth rate. The percent of increase is 100r. y = C (1 + r) t

You deposit $1500 in an account that pays 2.3% interest compounded yearly, 1)What was the initial principal (P) invested? 2)What is the growth rate (r)? The growth factor? 3)Using the equation A = P(1+r) t, how much money would you have after 2 years if you didn’t deposit any more money? 1)The initial principal (P) is $ )The growth rate (r) is The growth factor is

If a quantity decreases by the same proportion r in each unit of time, then the quantity displays exponential decay and can be modeled by the equation Where C = initial amount r = growth rate (percent written as a decimal) t = time where t  0 (1 - r) = decay factor where 1 - r < 1

W RITING E XPONENTIAL D ECAY M ODELS A quantity is decreasing exponentially if it decreases by the same percent in each time period. E XPONENTIAL D ECAY M ODEL C is the initial amount. t is the time period. (1 – r ) is the decay factor, r is the decay rate. The percent of decrease is 100r. y = C (1 – r) t

You buy a new car for $22,500. The car depreciates at the rate of 7% per year, 1)What was the initial amount invested? 2)What is the decay rate? The decay factor? 3)What will the car be worth after the first year? The second year? 1)The initial investment was $22,500. 2)The decay rate is The decay factor is 0.93.

Writing an Exponential Growth Model A population of 20 rabbits is released into a wildlife region. The population triples each year for 5 years.

A population of 20 rabbits is released into a wildlife region. The population triples each year for 5 years. b. What is the population after 5 years? Writing an Exponential Growth Model S OLUTION After 5 years, the population is P = C(1 + r) t Exponential growth model = 20(1 + 2) 5 = = 4860 Help Substitute C, r, and t. Simplify. Evaluate. There will be about 4860 rabbits after 5 years.

Writing an Exponential Decay Model C OMPOUND I NTEREST From 1982 through 1997, the purchasing power of a dollar decreased by about 3.5% per year. Using 1982 as the base for comparison, what was the purchasing power of a dollar in 1997? S OLUTION Let y represent the purchasing power and let t = 0 represent the year The initial amount is $1. Use an exponential decay model. = (1)(1 – 0.035) t = t y = C (1 – r) t y = Exponential decay model Substitute 1 for C, for r. Simplify. Because 1997 is 15 years after 1982, substitute 15 for t. Substitute 15 for t. The purchasing power of a dollar in 1997 compared to 1982 was $0.59.  0.59

1)Make a table of values for the function using x-values of –2, -1, 0, 1, and Graph the function. Does this function represent exponential growth or exponential decay?

This function represents exponential decay.

2) Your business had a profit of $25,000 in If the profit increased by 12% each year, what would your expected profit be in the year 2010? Identify C, t, r, and the growth factor. Write down the equation you would use and solve.

C = $25,000 T = 12 R = 0.12 Growth factor = 1.12

3) Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half- lives. Identify C, t, r, and the decay factor. Write down the equation you would use and solve.

C = 25 mg T = 4 R = 0.5 Decay factor = 0.5

Exponential Growth & Decay l.earnzillion.com/lessonsets/36 Exponential Growth & Decay Models learnzillion.com/lessons/256-model-exponential- growth-drawing-graphs-and-writing-equations Exponential Growth and_logarithmic_func/exp_growth_decay/v/exponential- growth-functions