'Exponential functions' diaporamas de présentation

Chapter 5: Exponential and Logarithmic Functions. 5.1 Inverse Functions 5.2 Exponential Functions 5.3 Logarithms and Their Properties 5.4 Logarithmic Functions 5.5 Exponential and Logarithmic Equations and Inequalities

Exponential Functions. L. Waihman 2002. A function that can be expressed in the form and is positive , is called an Exponential Function. Exponential Functions with positive values of x are increasing, one-to-one functions.

8.1 Exponential Growth. Algebra 2 Mrs. Spitz Spring 2007. Objective. Graph exponential growth functions Use exponential growth functions to model real-life situations, such as Internet growth. Assignment. Class Activity – Graphing Exponential Functions.

Maths Online. Exponential Functions. Why study graphs of exponential functions?. Maths Online. Radioactive Decay. Radioactive substance is dangerous because it decays and emits harmful radiation Radioactive substance will decay to half its mass over a period of time

Exponential Functions. Section 3.1. Objectives. Evaluate an exponential function at a given point. Determine the equation of an exponential function given a point or two points. Graph an exponential function. State the domain and range of an exponential function.

Algebra II. Mr. Hartzer, Hamtramck High School 2017-18. DO NOW: SAT Review.

Comparing Functions. Essential Questions. How do we compare properties of two functions? How do we estimate and compare rates of change?. Holt McDougal Algebra 2. Holt Algebra 2.

Logarithm (log). How do we know that 10 log 10 1000 = 10 x 3 ? Logarithmic and Exponential Functions Logarithmic and exponential functions are inverses of each other: If y = log b x then x = b y In words, log b x is the exponent you put on base b to get x . lol So,

Exponential Functions, Growth and Decay. 4-1. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 2. Holt Algebra 2. Warm Up Evaluate. 1. 100(1.08) 20 2. 100(0.95) 25 3. 100(1 – 0.02) 10 4. 100(1 + 0.08) –10. ≈ 466.1. ≈ 27.74. ≈ 81.71. ≈ 46.32. Objective.

Exponential Functions are functions which can be represented by graphs similar to the graph on the right. All base exponential functions are similar because they all go through the point (0,1), regardless of the size of their base number. Exponential Functions are written in the form: y = ab x

3.2 Inverse Functions and Logarithms. 3.3 Derivatives of Logarithmic and Exponential functions. One-to-one functions. Definition: A function f is called a one-to-one function if it never takes on the same value twice; that is f(x 1 ) ≠ f(x 2 ) whenever x 1 ≠ x 2 .

Real-Valued Functions of a Real Variable and Their Graphs. Lecture 43 Section 9.1 Wed, Apr 18, 2007. Functions. We will consider real-valued functions that are of interest in studying the efficiency of algorithms. Power functions Logarithmic functions Exponential functions.

Chapter 4 The Exponential and Natural Logarithm Functions. Chapter Outline. Exponential Functions The Exponential Function e x Differentiation of Exponential Functions The Natural Logarithm Function The Derivative ln x Properties of the Natural Logarithm Function. § 4.1.

Graphs of Exponential Functions. Lesson 3.3. How Does a*b t Work?. Given f(t) = a * b t What effect does the a have? What effect does the b have? Try graphing the following on the same axes 3 * 1.1 X 0.75 * 1.1 X 2 * 1.1 X 0.5 * 1.1 X 1.5 * 1.1 X.

Chapter 9. Rational Numbers and Real Numbers, with an Introduction to Algebra. 9.1 The Rational Numbers. The set of rational numbers is the set. Definition : Equality or Rational Numbers if and only if Theorem : Let be any rational number and n any nonzero integer. Then .

Domain: (- ∞,∞) y -intercept is the point (0, 1) Continuous Increasing if a > 1. Range: (0, ∞) No x -intercept Horizontal asymptote y =0 Decreasing if a < 1. Characteristics of Exponential Functions f ( x ) = a x.

3.1 Exponential Functions and their Graphs. Students will recognize and evaluate exponential functions with base a. Students will graph exponential functions. Students will recognize, evaluate, and graph exponential functions with base e.

Lecture 14. Introduction to dynamic systems Energy storage Basic time-varying signals Related educational materials : Chapter 6.1, 6.2. Review and Background. Our circuits have not contained any energy storage elements Resistors dissipate energy

8-2 Properties of Exponential Functions. p. 431. Do Now. Does the function represent growth or decay? What is the percent of increase or decrease?. GROWTH. a = 5. b = 3/2. GREATHER THAN 1!. Example 1 Graph. Make a table of values for ANY exponential function!. e.

5.1 – Exponential Functions. Exponential Function = a type of function in which a constant is raised to a variable power Many real-life applications using exponential functions Exponential functions will be of the form : f(x) = a x. Behavior.