Exponential Functions

Slides:

Advertisements

Similar presentations

Exponential Functions Section 3.1. Objectives Evaluate an exponential function at a given point. Determine the equation of an exponential function given.

Advertisements

A Dash of Limits. Objectives Students will be able to Calculate a limit using a table and a calculator Calculate a limit requiring algebraic manipulation.

Warm Up 1. 5x – 2 when x = – t 2 when 3. when x = Give the domain and range for this relation: {(1, 1), (–1, 1), (2, 4), (–2, 4),

Section 10.1 The Algebra of Functions. Section 10.1 Exercise #1 Chapter 10.

Objectives:  Understand the exponential growth/decay function family.  Graph exponential growth/decay functions.  Use exponential function to models.

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

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

Warm Up/Review Function and Inverse

Algebra 1 Step 2: Plot the points for the ordered pairs. Step 3: Join the points to form a line. Lesson 5-3 Model the function rule y = + 2 using a table.

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

Zero and Negative Exponents

Exponents and Exponential Functions

Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.

Holt Algebra Exponential Functions, Growth, and Decay Warm Up Evaluate (1.08) (0.95) (1 – 0.02) ( ) –10.

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

Section 8 – 7 Exponential Functions Objectives: To evaluate exponential functions To graph exponential functions.

Do Now (7.4 Practice): Graph. Determine domain and range.

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.

Lesson 3.2 Read: Pages Handout 1-49 (ODD), 55, 59, 63, 68, (ODD)

Pre-Calc Lesson 5-2 Growth and Decay: Rational Exponents Rational Exponents: ( Fractions as exponents) b 1/q = q b 1 so b p/q = q b p Simplify: /4.

Logarithmic Functions

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.

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

Wednesday, March 4 Use the Rule of 72 to find the length of time to double investments. Graph Reciprocal Functions on a coordinate system.

Algebra I Ch. 7 Warm-ups. Section 7-1 WU, Day 1 Graph the following systems of linear inequalities (sketch a graph on your paper) 1. y < ¼ x – 32. y

Warm up Simplify the following: 1.) 2.) 3.) 4.). Chapter 8.7 Exponential Functions.

Rational Functions Essential Questions

Algebra 1 Relations and Functions A Relation is a set of ordered pairs. The Domain of a relation is the set of first coordinates of the ordered pairs.

Exponential Functions,

Minds On Unit 7: Exponential Functions The answer to a power is 9. What might the power be?

Integers and Absolute Value COURSE 3 LESSON 1-3 Graph the points 2, –3, and 1 on a number line. 1-3.

How do we solve exponential and logarithmic equations and equalities?

Solving Equations Exponential Logarithmic Applications.

Algebra II 8-1 (2). Starter: Graph: y = 2(4) x+3 -2 Asymptote: Domain: Range:

Lesson 45: Exponents, The Rules

Notes Over 1.2.

Algebra 2cc Section 5.3 Define and apply the number “e”.

Find the solution of the exponential equation, correct to four decimal places. e x =

Ch. 8.5 Exponential and Logarithmic Equations

4-1 Exponential Functions, Growth and Decay Warm Up

12.2 Finding Limits Algebraically

Algebra 1 Section 2.3 Subtract real numbers

Exponential Functions, Growth and Decay

SECTION 7-6 : EXPONENTIAL FUNCTIONS

The Natural Base, e Essential Questions

Exponential Functions

Write down all the laws of indices

Function Rules, Tables, and Graphs

Graphing Square Root Functions

Relations and Functions

4-1 Exponential Functions, Growth and Decay Warm Up

Algebra Exponentials Jeopardy

4-1 Exponential Functions, Growth and Decay Warm Up

Chapter 7 Functions and Graphs.

Multiplying Powers with the Same Base

Relations and Functions

Notes Over 8.3 Simplifying Natural Base Expressions

4-1 Exponential Functions, Growth and Decay Warm Up

Check Skills/Warm Ups Graph each function.

EXPONENTIAL FUNCTION where (base) b > 0 and b For 0 < b < 1,

7-1 Exponential Functions, Growth and Decay Warm Up

Exponential Functions, Growth and Decay

Lesson Quizzes Standard Lesson Quiz

Warm-Up Honors Algebra /17/19

Jeopardy Choose a category. Click to begin..

Warm Up Evaluate if x = 4 if ƒ(x) = 2x – 5 and g(x) = x² ƒ(g(x))

Notes Over 8.7 Writing an Exponential Function

Domain & Range Algebra 1, Unit 3, Lesson 3.

7-1 Exponential Functions, Growth and Decay Warm Up

Presentation transcript:

Exponential Functions ALGEBRA 1 LESSON 8-7 Evaluate each exponential function. a. y = 3x for x = 2, 3, 4 x y = 3x y 2 32 = 9 9 3 33 = 27 27 4 34 = 81 81 b. p(q) = 3 • 4q for the domain {–2, 3} q p(q) = 3 • 4q p(q) –2 3 • 4–2 = 3 • = 1 16 3 3 3 • 43 = 3 • 64 = 192 192 6-2

Exponential Functions ALGEBRA 1 LESSON 8-7 Suppose two mice live in a barn. If the number of mice quadruples every 3 months, how many mice will be in the barn after 2 years? ƒ(x) = 2 • 4x ƒ(x) = 2 • 48 In two years, there are 8 three-month time periods. ƒ(x) = 2 • 65,536 Simplify powers. ƒ(x) = 131,072 Simplify. 6-2

Exponential Functions ALGEBRA 1 LESSON 8-7 Graph y = 2 • 3x. 2 2 • 32 = 2 • 9 = 18 (2, 18) x y = 2 • 3x (x, y) –2 2 • 3–2 = = (–2, ) 2 3 2 9 –1 2 • 3–1 = = (–1, ) 2 31 3 0 2 • 30 = 2 • 1 = 2 (0, 2) 1 2 • 31 = 2 • 3 = 6 (1, 6) 6-2

Exponential Functions ALGEBRA 1 LESSON 8-7 The function ƒ(x) = 1.25x models the increase in size of an image being copied over and over at 125% on a photocopier. Graph the function. x ƒ(x) = 1.25x (x, ƒ(x)) 1 1.251 = 1.25 1.3 (1, 1.3) 2 1.252 = 1.5625 1.6 (2, 1.6) 5 1.255 = 3.0518 3.1 (5, 3.1) 4 1.254 = 2.4414 2.4 (4, 2.4) 3 1.253 = 1.9531 2.0 (3, 2.0) 6-2

Exponential Functions ALGEBRA 1 LESSON 8-7 1. Evaluate each function rule for the given value. a. y = 0.5x for x = 3 b. ƒ(x) = 4 • 3x for x = –2 2. Suppose an investment of $5000 doubles every 12 years. a. How much is the investment worth after 24 years? b. After 48 years? 0.125 4 9 $20,000 $80,000 3. Graph y = 0.5 • 3x. 4. Graph y = –0.5 • 3x. 6-2