CHAPTER 5 REVIEW Exponential and Logarithmic Functions.

Slides:

Advertisements

Similar presentations

EXPONENTIAL GROWTH Exponential functions can be applied to real – world problems. One instance where they are used is population growth. The function for.

Advertisements

Logarithmic Functions Section 3.2. Objectives Rewrite an exponential equation in logarithmic form. Rewrite a logarithmic equation in exponential form.

Exponential and Logarithmic Functions

4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.

 Growth: interest, births  Decay: isotopes, drug levels, temperature  Scales: Richter, pH, decibel levels Exponential and Logarithm Functions Functions.

5.2 Logarithmic Functions & Their Graphs

Pre-Calc Lesson 5-5 Logarithms

Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.

8.1 Exponential Growth Goal: Graph exponential growth functions.

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)

LOGARITHMS AND EXPONENTIAL MODELS

Evaluating logarithms

7.4 Logarithms p. 499 Evaluate logarithms Graph logarithmic functions

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 4 Exponential and Logarithmic.

Sullivan PreCalculus Section 4.4 Logarithmic Functions Objectives of this Section Change Exponential Expressions to Logarithmic Expressions and Visa Versa.

Aim: What is the natural logarithms? Do Now: HW: p.338 # 8,16,20,26,30,38,42,48,50,52,56,58 Given f(x) = e x write the inverse function.

Lesson 5-5 Logarithms. Logarithmic functions The inverse of the exponential function.

Welcome! The Topic For Today Is…. Exponential and Logarithmic Equations Exponential Functions Logarithmic Functions Expanding Expressions Condensing Expressions.

Exponential Functions 4.2 Explorations of growth and decay.

20. Exponential Functions

Exponential and 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)

Section 6.4 Solving Logarithmic and Exponential Equations

Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

5.5 Logarithmic Functions Objective To Define and apply logarithms.

Section 6.3 – Exponential Functions Laws of Exponents If s, t, a, and b are real numbers where a > 0 and b > 0, then: Definition: “a” is a positive real.

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

Quiz 7-1: 1. Where does the graph cross the y-axis? 2. f(1) = ? 3. Horizontal asymptote = ? 4. How was the function transformed to get f(x) above? to get.

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

Holt Algebra Exponential Functions, Growth, and Decay Holt Algebra 2 Read each slide. Answer the hidden questions. Evaluate (1.08) (0.95)

Graphing Exponentials and Logs

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

Aim: What is the exponential function? Do Now: Given y = 2 x, fill in the table x /8 ¼ ½ y HW: Worksheet.

R—05/28/09—HW #73: Pg 477:47,49,50; Pg 490:17,49-61odd; Pg 496:31-55 eoo; Pg 505:25-59 odd 50) V=22000(.875)^t; 14,738.

Copyright © 2009 Pearson Education, Inc. Slide Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

Section 6 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Exponential and Logarithmic Equations; Further Applications.

Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1

The number e is ________________ It is also known as Euler’s number Irrational.

5.2 Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,

Notes Over 5.2 Rewriting Logarithmic Equations and Rewrite the equation in exponential form. are equivalent. Evaluate each logarithm.

4.3 – Logarithmic functions

Applications of Common Logarithms Objective: Define and use common logs to solve exponential and logarithmic equations; use the change of base formula.

TEST TOMORROW 3/1/ NON-CALCULATOR MULTIPLE CHOICE 15-FREE RESPONSE QUESTIONS Unit 2 review.

Review Exponential + Logarithmic Functions Math Analysis.

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.

Exponential Functions Chapter 10, Sections 1 and 6.

4.2 Logarithmic Functions

February 13, 2012 At the end of today, you will be able to graph a logarithmic function. Warm-up: Describe the transformation for: f(x) = -3 x.

(a) (b) (c) (d) Warm Up: Show YOUR work!. Warm Up.

7-1 Exponential Functions

SOLVING LOGARITHMIC EQUATIONS. STEPS: 1.Get the LOG, LN, or e expression alone. 2. Convert to the opposite form. Logarithmic ---> Exponential Exponential.

LEQ: How do you evaluate logarithms with a base b? Logarithms to Bases Other Than 10 Sec. 9-7.

Over Lesson 7–4 5-Minute Check 1 A.3.3 × 10 4 B × 10 4 C × 10 6 D × 10 7 What is 3,352,000 in scientific notation?

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

9.1, 9.3 Exponents and Logarithms

Graphing $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $ 300 $ 200 $ 400 $ 500 $ 100 $300 $ 200 $ 400.

LEQ: What is the process used to evaluate expressions containing the natural logarithm?

Section 3 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Logarithmic Functions Define a logarithm. Convert between.

5.2 L OGARITHMIC F UNCTIONS & T HEIR G RAPHS Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,

Slide the Eraser Exponential and Logarithmic Functions.

Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.

6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate.

Sullivan Algebra and Trigonometry: Section 6.4 Logarithmic Functions

Sullivan Algebra and Trigonometry: Section 6.3

Logarithmic Functions and Their Graphs

A function is given by a formula. Determine whether it is one-to-one

THE LOGARITHMIC FUNCTION

6.3 Logarithms and Logarithmic Functions

Presentation transcript:

CHAPTER 5 REVIEW Exponential and Logarithmic Functions

Directions You need a piece of paper (or dry erase board), a pencil (or marker), & a calculator. You need a piece of paper (or dry erase board), a pencil (or marker), & a calculator. We will go through a series of review problems, solving them and then reviewing them as a class. Each slide will take 1 to 2 minutes. We will go through a series of review problems, solving them and then reviewing them as a class. Each slide will take 1 to 2 minutes.

1 Evaluate a. log (100) = b. log = c. log = 2 7 1/9

2 Solve (nearest 100 th ) a. 7 x = 343 b. 12 a+1 = 1000 c. (0.4) w = e x = 3 a = 1.78 w = -1.09

3 Solve. Nearest Hundredth a. log x = 2.91 b. 2 ln 15 = ln x c. log x 64 = 3 x = x = 225 x = 4

4 (evaluate) a. log 97, 234 = b. ln 10 = c. ln (-4.1) = undefined! W H Y ?

5 For the graph of f(x) = e x a. Give the domain. b. Give the range. c. Name the asymptote(s). All reals Positive reals x - axis

6 Given y = ab x When is the equation a. growth? b. decay? when b > 1 when 0< b < 1

7 Write in exponential form: a. ln (6.28) = 1.8 b. log 6 = e 1.8 = = 1 216

8 Strontium 90 has a half-life of 29 years. How much will be left of 5 grams after 116 years? y = 5 (.5 ) (116/29) = grams

9 Rewrite as the log of a single quantity. a. log x – log y b. 2 ln 5 + ln 10 c. 3 log 2 – log 4 log x y ln 250 log 2

10 A new car costing $13,000 is predicted to depreciate at a rate of 12% per year. How much will the car be worth in 7 years? 13,000 (.88) 7 = $5,

11 The population of a strain of bacteria grows according to N = N o (3) 0.827t where t is the time in hours. How long will it take for 30 bacteria to increase to 500 bacteria? 3.10 hours

12 Consider y = 2 x and y = 5 x. a. Name three things the graphs have in common. b. Which graph is growing more quickly? How do you know? same y-intercept: (0, 1), exponential growths, x-axis is asymptote y = 5 x because 5 > 2

Tonight…… STUDY!!!!! R E M E M B E R …. There will be a non-calculator part to the test!