Section 3-11 Bell Quiz Ch 3a 10 pts possible 2 pts

Section 3-12 Chapter 3 Exponential, Logistic, and Logarithmic Functions

Section 3-13 Ch 3 Overview Just like their algebraic cousins, exponential, logistic, and logarithmic functions have wide application. Exponential functions model growth and decay over time, such as unrestricted population growth and the decay of radioactive substances. Logistic functions model restricted population growth, certain chemical reactions, and the spread of rumors and diseases. Logarithmic functions are the basis of the Richter scale of earthquake intensity, the pH acidity scale, and the decibel measurement of sound..

Section 3-14 Ch 3 Overview The chapter closes with a study of the mathematics of finance, an application of exponential and logarithmic functions often used when making investments.

Section Exponential and Logistic Functions

Section 3-16 What you’ll learn about Exponential Functions and Their Graphs The Natural Base e Population Models … and why Exponential and logistic functions model many growth patterns, including the growth of human and animal populations.

Section 3-17 Exponential Functions Let a and b be real number constants. An exponential function in x is a function that can be written in the form, where b is positive, and. The constant a is the initial value of f (the value at x = 0), and b is the base.

Section 3-18 Recognizing Exponential Functions Which of the following are exponential functions?

Section 3-19 Computing Exponential Function Values Find: f (4) = f (0) = f (-3) = Makes a graph (x, y) values.

Section Graphing Activity Graphs of y = b x What do they have in common? Window: x-min: -5 y-min: -1 x-max: 5y-max: 5

Section Generalized y = b x Domain: Range: Vertical/horizontal asymptote Intercept: Function is increasing Bounded?

Section Transforming Exponential Functions Vertical Translations y = f(x) ± c: + up c units - down c units Horizontal Translations y = f(x ± c): + left c units - right c units Across the x-axis y = -f(x) Across the y-axis y = f(-x) Vertical Stretch or Shrink y = k·f(x): 0 < k < 1: V. Shrink k > 1: V. Stretch Horizontal Stretch or Shrink y = f(k·x): 0 < k < 1: H. Stretch k > 1: H. Shrink

Section Example Transforming Exponential Functions Describe how to transform the graph of Right 1 Reflects across the y-axis Vertical Stretch of 3 Horizontal Shrink of 2 and reflects across the y-axis Down 1

Section The Natural Base e Or e is like π e = F(x) = e x is the natural exponential function because of its applications in Calculus.

Section Exponential Functions and the Base e

Section Exponential Functions and the Base e

Section Example Transforming Exponential Functions = same as other exponential functions

Section Population Growth Using 20 th century U.S. census data, the population of New York state can be modeled by where P is the population in millions and t is the number of years since Based on this model, (a) What was the population of New York in 1850? (b) What will New York state’s population be in 2010? 1,794,558 19,161,673

Section HOMEWORK Section 3-1 (page286) 1 - 4, , , 55, 57