Day 4: Applications of Graphing Exponential Functions

Slides:

Advertisements

Similar presentations

Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION.

Advertisements

MODELING REAL SITUATIONS USING EXPONENTIAL FUNCTIONS: PART 1 Patterns #4.

The number of ants at a picnic is growing rapidly. At 11am 5 ants find the picnic. Each hour after 11am, 3 times as many ants have found the picnic. Let.

Exponential Functions

EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.

6.6 Logarithmic and Exponential Equations

Section 6.2 Exponential Function Modeling and Graphs.

8.2 Exponential Decay P Exponential Decay Has the same form as growth functions f(x) = ab x Where a > 0 BUT: 0 < b < 1 (a fraction between 0 & 1)

3.2 Graph Exponential Decay Functions P. 236 What is exponential decay? How can you recognize exponential growth and decay from the equation? What is the.

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.

Graph Exponential Growth Functions

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 344 Chapter Review Compute the exact value of the.

Topic 2: Linear Equations and Regression

SECTION Growth and Decay. Growth and Decay Model 1) Find the equation for y given.

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.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 8-6 Exponential and Logarithmic Functions, Applications, and Models.

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.

CHAPTER 1: PREREQUISITES FOR CALCULUS SECTION 1.3: EXPONENTIAL FUNCTIONS AP CALCULUS AB.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 4 Inverse, Exponential, and Logarithmic Functions Copyright © 2013, 2009, 2005 Pearson Education,

Exponential Functions Topic 2: Solving 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)

Graph y = b for 0 < b < 1

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

Over Lesson 7–5 5-Minute Check 1 The graph of y = 4 x is shown. State the y-intercept. Then use the graph to approximate the value of Determine.

Solving Exponential Equations II LG: I can use trial and error to solve exponential equations.

Compound Interest 8.2 Part 2. Compound Interest A = final amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of.

8.2 – Properties of Exponential Functions

Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.

Chapter 1.3 Exponential Functions. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)

Exponential Growth & Decay Objective: Be able to graph and find equations of exponential equations. TS: Explicitly assess information and draw conclusions.

AII, 12.0: STUDENTS KNOW THE LAWS OF FRACTIONAL EXPONENTS, UNDERSTAND EXPONENTIAL FUNCTIONS, AND USE THESE FUNCTIONS IN PROBLEMS INVOLVING EXPONENTIAL.

Exponential Functions

Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.

Section 6.1 Percent Growth. Upon receiving a new job, you are offered a base salary of $50,000 plus a guaranteed raise of 5% for each year you work there.

8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

Graphing Exponential Growth Functions

Warm-Up 1.5 –2 Evaluate the expression without using a calculator. ANSWER –24 4. State the domain and range of the function y = –(x – 2)

MODELING REAL SITUATIONS USING EXPONENTIAL FUNCTIONS Patterns #4 & 5.

8.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write and Graph Exponential Decay Functions.

Section 9.3 We have previously worked with exponential expressions, where the exponent was a rational number The expression b x can actually be defined.

Graphing Exponential Decay Functions In this lesson you will study exponential decay functions, which have the form ƒ(x) = a b x where a > 0 and 0 < b.

9.1 Exponential Functions

What do you see?. Warm-up (Hint: not all answer will be used) 1.Which equations below model exponential growth? 2.Which equations model exponential decay?

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 4.5, Slide 1 Chapter 4 Exponential Functions.

Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.

Exponential Decay Functions 4.2 (M3) p Warm-Up Evaluate the expression without using a calculator. ANSWER –1 ANSWER –3 2.– ANSWER.

Exploring Exponential Models

EXAMPLE 3 Graph y = ab + k for 0 < b < 1 x – h Graph y = 3 –2. State the domain and range. 1 2 x+1 SOLUTION Begin by sketching the graph of y =, which.

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

Exponential Growth and Decay Formula:

Chapter 8: Exploring Exponential Models. What is an exponential equation? An exponential equation has the general form y=ab x.

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

How do I graph and use exponential growth and decay 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.

Goal 4.03: Systems of Equations and Inequalities.

Warm-Up Exercises Evaluate the expression without using a calculator. ANSWER –1 ANSWER –3 2.–

Warm Up Use the table to estimate the population for the year U.S Population according to census data. YearPopulation (millions)

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

Chapter 7 Section 1. EXAMPLE 1 Graph y = b for b > 1 x SOLUTION Make a table of values.STEP 1 STEP 2 Plot the points from the table. Graph y =. x 2.

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

Lesson 8.2 Exponential Decay. Lesson 8.2 Exponential Decay.

Chapter 7 Section 2. EXAMPLE 1 Graph y = b for 0 < b < 1 x Graph y = 1 2 x SOLUTION STEP 1 Make a table of values STEP 2 Plot the points from the table.

8.1 & 8.2 Exponential Growth and Decay 4/16/2012.

Chapter 5: Inverse, Exponential, and Logarithmic Functions

8.1 Exploring Exponential Models

GRAPH EXPONENTIAL DECAY FUNCTIONS

Write the percent as a decimal.

Presentation transcript:

Day 4: Applications of Graphing Exponential Functions

Compound Interest Suppose you make a long-term investment of $1000 at a fixed interest rate of 8% compounded annually. The amount A dollars of your investment after n years is represented by the equation

Light Transmission Through Glass Several layers of glass are stacked together. Each layer reduces the light passing through it by 5%. The percent P of light passing through n layers is represented by the equation

Comparing the Equations The two situations are examples of Exponential Growth and Exponential Decay Exponential Growth Exponential Decay Initial Value Decay Factor (Less than 1) Initial Value Growth Factor (Greater than 1)

Graphing Exponential Functions There are two ways in which we will graph exponential functions: Using a graphing calculator Using a table of values, paper and pencil

Example 1: Using a Graphing Calculator The first artificial satellites were put in orbit in the late 1950s. The cumulative mass, c tonnes, of all the satellites in orbit can be modelled as a function of n, the number of years since 1960 by the equation:

a) Graph the equation using a graphing calculator Use appropriate window settings. What makes sense? Try:

b) Estimate the cumulative mass in 1969, the year when a person first walked on the moon? Two ways of solving: Use the graph to estimate Substitute 9 for n in the equation Answer: Approx 333 tonnes

c) According to the model, when did the cumulative mass become 4000 t? Two ways of solving: Use the trace function on your graphing calculator to trace to the point where the y-coordinate is closest to 4000 2. Graph y = 4000 and find the point of intersection of the two graphs Answer: Approx 31 years after 1960 or 1991

Example 2: Using a Table of Values Coffee, tea, cola, and chocolate contain caffeine. When you consume caffeine, the percent, P, left in your body can be modelled as a function of the elapsed time, n hours, be the equation:

a) Use a table of values and graph the equation. What would the domain and range be? Use this to determine what numbers to use in your table of values.

b)Determine how long it takes until only 20% of the caffeine remains. Use your graph to estimate. Answer: Approx 11 - 12 hours

Homework Complete the handout during class time. If you are unable to complete it during this time, you must complete all graphs at home by hand.