Get ready before the bell rings!  Take out your homework to prepare for the homework quiz.  Check the file folder for your class to pick up graded work.

Slides:

Advertisements

Similar presentations

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

Advertisements

Exploring Exponential Growth and Decay Models

Exponential Functions

TODAY IN ALGEBRA…  Learning Target : 8.5 You will write and graph exponential growth models.  Independent Practice.

7.1 Notes – Modeling Exponential Growth and Decay

Exponential Growth and Decay Functions. What is an exponential function? An exponential function has the form: y = ab x Where a is NOT equal to 0 and.

TODAY IN ALGEBRA…  Warm up: Sequences  Learning Target 1: 8.6 You will write and graph exponential decay functions.  Learning Target 2: You will use.

How does one Graph an Exponential Equation?

4-1 exponential functions, growth and decay

Get ready before the bell rings!

8.3 The number e p. 480 What is the Euler number? How is it defined? Do laws of exponents apply to “e” number? How do you use “e” on your calculator? When.

Objectives Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.

Exploring Exponential Growth and Decay Models Sections 8.5 and 8.6.

Holt Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.

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

Definition: One-to-one Function

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.

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, ∞)

Warm Up Evaluate (1.08) (0.95) (1 – 0.02)10

Use mental math to evaluate.

Evaluate (1.08) (0.95) (1 – 0.02) ( )–10.

Graph Horizontal Asymptote: y = -1 Domain: Range:y > -1 all real numbers a = ____ 2 b= ____ 3 h = ____ 2 k = ____.

Chapter 8 Slide the Eraser. Question 1 write the following using exponents? 7 · 7 2 · 2 · 2 x · x · x· x · x· x · x.

8.8 Exponential Growth. What am I going to learn? Concept of an exponential function Concept of an exponential function Models for exponential growth.

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

State the domain and range of each function Exponential Growth and Decay.

Exponential Functions What You Will Learn How to graph exponential functions And how to solve exponential equations and inequalities.

Opener-NEW SHEET-11/29 Evaluate (1.08) (0.95)25

Objective Write and evaluate exponential expressions to model growth and decay situations.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Digital Lesson.

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

Algebra II w/ trig. Exponential Functions – has the form y= ab x, where a ≠0, b>0, and b≠1 - y represents the quantity after time is expired - a represents.

Get ready before the bell rings! Take out homework and a pencil to prepare for the homework quiz! Send one person to get textbooks for your table. Check.

Exploring Exponential Functions. Exponential Function The independent variable (x) is an exponent. f(x) = a b x “a” cannot be zero, “b” cannot be one.

Get ready before the bell rings! Take out homework and a pencil to prepare for the homework quiz! Check the file folder for your class to pick up graded.

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.

Exploring Exponential Growth and Decay Models Acc. Coordinate Algebra / Geometry A Day 57.

9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u

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

Section 3.1 Exponential Functions. Definition An exponential function is in the form where and.

Holt McDougal Algebra Exponential Functions, Growth, and Decay 4-1 Exponential Functions, Growth and Decay Holt Algebra 2 Warm Up Warm Up Lesson.

Holt Algebra Exponential Functions, Growth, and Decay 7-1 Exponential Functions, Growth and Decay Holt Algebra 2 Warm Up Warm Up Lesson Presentation.

7.1 E XPONENTIAL F UNCTIONS, G ROWTH, AND D ECAY Warm Up Evaluate (1.08) (1 – 0.02) ( ) –10 ≈ ≈ ≈ Write.

Holt McDougal Algebra 2 Exponential Functions, Growth, and Decay Exponential Functions, Growth and Decay Holt Algebra 2Holt McDougal Algebra 2 How do.

EXPONENTIAL FUNCTIONS Section TOPIC FOCUS I can… Identify exponential growth and decay Graph exponential functions.

8-1: Exponential Growth Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions in.

Warm Up Evaluate (1.08) (0.95) (1 – 0.02) ( ) –10 ≈ ≈ ≈ ≈

Ch. 4.4 to 4.5. “a” changes the steepness of the growth or decay If (-a) graph is flipped “b” is the base it determines if it is an EXPONENTIAL GROWTH.

Holt McDougal Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic.

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.

Homework Quiz. Rule of 72 Interest Rate 8% 12% 6% 2%.03% Years for money to double 9 years years.

4.3 Use Functions Involving e PROJECT DUE: Tomorrow Quiz: Tomorrow Performance Exam: Friday *We will be having a book check tomorrow…. BRING BOTH.

Holt McDougal Algebra Exponential Functions, Growth, and Decay Warm Up Evaluate (1.08) (0.95) (1 – 0.02) ( )

Holt Algebra Exponential Functions, Growth, and Decay exponential function baseasymptote exponential growth and decay Vocabulary Write and evaluate.

8-3: The Number ‘e’ (Day 1) Objective (Ca. Standard 12): Students know the laws of fractional exponents, understand exponential function, and use these.

3.1 Exponential Functions. Mastery Objectives Evaluate, analyze, and graph exponential functions. Solve problems involving exponential growth and decay.

Chapter 7 Exponential and Logarithmic Functions. 7-1 Exponential Growth.

Graphs of Exponential Functions. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

Bellwork 1) 2) 3) 4). Lesson 7.1 Graph Exponential Growth Functions.

DAY 5 – EXPONENTIAL GROWTH AND DECAY. ZOMBIES! A rabid pack of zombies is growing exponentially! After an hour, the original zombie infected 5 people.

6.1 Exponential Functions

Determine all of the real zeros of f (x) = 2x 5 – 72x 3 by factoring.

Check it out! Domain and Range of Exponential Functions

Module 10: Lesson 10.2 Graphing Exponential Functions

4.3 Use Functions Involving e

Warm-up 5/22/2019 Day 6.

Presentation transcript:

Get ready before the bell rings!  Take out your homework to prepare for the homework quiz.  Check the file folder for your class to pick up graded work.

5.17 GRAPHS OF EXPONENTIAL FUNCTIONS Chapter 5: Exponents & Functions Helpful Links

Exponential Functions  There are two types of exponential behavior, exponential growth and exponential decay.

For Discussion y=a(b x )  What values of b lead to exponential growth? To exponential decay? Test some positive values of b and make a conjecture.  Values of b greater than 1 lead to exponential growth. Values of b greater than 0 but less than 1 lead to exponential decay.

Graphs of Exponential Functions  You know that exponents can be positive, negative, or zero. In fact, exponential functions can take any real number as input. In some cases, depending on the situation that an exponential function represents, it may not make sense to allow negative numbers as input.  The graph shows the exponential function f(x) = 3 x  What is the domain? Range? Domain is all real numbers. Range: y > 0

Example  Alicia and Berta both save $2500.  Alicia’s Plan: Alicia saves her money in a jar. She will add $200 every year.  Berta’s Plan: Berta saves her money in the bank, earning 6% interest each year compounded annually.  Who will have more money after 5 years? After 15 years?  Alicia will have more money after 5 years. Berta will have more after 15 years.

Experiment  Randomly toss the algebra tiles onto the table from the cup.  Count the number of “Red” survivors. Remove all others.  Return only the survivors into the cup and repeat 6 times. Make a table to record your results. Toss NumberNumber of Survivors