'Exponential functions' diaporamas de présentation

Real-Valued Functions of a Real Variable and Their Graphs

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.

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4-1

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Chapter 9

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 .

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Algebra II

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

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Lecture 14

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

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8.1 Exponential Growth

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Exponential Functions

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.

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Chapter 5: Exponential and Logarithmic Functions

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

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Exponential Functions are functions which can be represented by graphs similar to the graph on the right

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

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Comparing Functions

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.

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3.2 Inverse Functions and Logarithms

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 .

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3.1 Exponential Functions and their Graphs

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.

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Graphs of Exponential Functions

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.

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Exponential Functions

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.

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Chapter 4 The Exponential and Natural Logarithm Functions

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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

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8-2 Properties of Exponential Functions

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.

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Logarithm (log)

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,

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Characteristics of Exponential Functions f ( x ) = a x

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.

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