Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 296 Tell whether the function is an exponential growth or an exponential decay function and find the constant percentage rate of growth or decay. 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 2 Homework, Page 296 Tell whether the function is an exponential growth or an exponential decay function and find the constant percentage rate of growth or decay. 5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 3 Homework, Page 296 Determine the exponential function that satisfies the given conditions. 9.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 4 Homework, Page 296 Determine the exponential function that satisfies the given conditions. 13.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 5 Homework, Page 296 Determine the exponential function that satisfies the given conditions. 17.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 6 Homework, Page 296 Determine a formula for the exponential function whose graph is given. 21.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 7 Homework, Page 296 Find the logistic function that satisfies the given conditions. 25.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 8 Homework, Page 296 Find the logistic function that satisfies the given conditions. 25.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 9 Homework, Page The 2000 population of Jacksonville, FL was 736,000 and was increasing at the rate of 1.49% each year. At that rate, when will the population be one million?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The 2000 population of Jacksonville, FL was 736,000 and was increasing at the rate of 1.49% each year. At that rate, when will the population be one million?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The half-life of a radioactive substance is 14 days. there are 6.6 g initially. a. Express the amount of the substance remaining as a function of time t. b. When will there be less than 1 g remaining? After 39 days.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Using the population model that is graphed, explain why the time it takes the population to double is independent of the population size.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Determine the atmospheric pressure outside an aircraft flying at 52,800 ft (10 miles above sea level).
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The number of students infected with flu at Springfield High after t days is modeled by the function: A. What was the initial number of infected students? B.When will the number of infected students be 200? C. The school will close when 300 of the 800-student body are infected. When will the school close?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page B.When will the number of infected students be 200? C. The school will close when 300 of the 800- student body are infected. When will the school close?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page What is the constant percentage growth rate of a.49% b.23% c.4.9% d.2.3% e.1.23%
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page a. Use the data in the table and logistic regression to predict the population in The logistic model predicts a population of million people in the year b. Compare the prediction with the value listed in the table for The model underestimates the population by 0.3 million people. c. Which model, logistic or exponential makes the better prediction in this case? The logistic model makes a much more accurate estimate than the exponential model (overestimates by 3 million).
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.3 Logarithmic Functions and Their Graphs
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Inverses of Exponential Functions Common Logarithms – Base 10 Natural Logarithms – Base e Graphs of Logarithmic Functions Measuring Sound Using Decibels … and why Logarithmic functions are used in many applications, including the measurement of the relative intensity of sounds.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Changing Between Logarithmic and Exponential Form
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Inverses of Exponential Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Basic Properties of Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Evaluating Logarithms Evaluate the logarithmic expression without using a calculator.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide An Exponential Function and Its Inverse
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Common Logarithm – Base 10 Logarithms with base 10 are called common logarithms. The common logarithm log 10 x = log x. The common logarithm is the inverse of the exponential function y = 10 x.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Basic Properties of Common Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Solving Simple Logarithmic Equations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Basic Properties of Natural Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Evaluating Natural Logarithms Evaluate the logarithmic expressions:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Graphs of the Common and Natural Logarithm
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Drawing Logarithmic Graphs Draw the graph of the given function:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Transforming Logarithmic Graphs
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Decibels
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Computing Decibel Levels Compute the decibel levels of the following Subway train Threshold of pain
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Review Section 3.3 Page 308, Exercises: 1 – 65 (EOO), 59
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.4 Properties of Logarithmic Functions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Properties of Logarithms Change of Base Graphs of Logarithmic Functions with Base b Re-expressing Data … and why The applications of logarithms are based on their many special properties, so learn them well.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Properties of Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Proving the Product Rule for Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Expanding the Logarithm of a Product
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Expanding the Logarithm of a Quotient
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Change-of-Base Formula for Logarithms
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Evaluating Logarithms by Changing the Base
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Graphing Logarithmic Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Re-Expression of Data If we apply a function to one or both of the variables in a data set, we transform it into a more useful form, e.g., in an earlier section we let the numbers 0 – 100 represent the years 1900 – Such a transformation is called a re-expression.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Re-Expressing Kepler’s Third Law Re-express the (a, T) data points in Table 3.20 as (ln a, ln T) pairs. Find a linear regression model for the re-expressed pairs. Rewrite the linear regression in terms of a and T, without logarithms or fractional exponents. PlanetAvg Dist (AU)Period (years) Mercury Venus Earth Mars Jupiter Saturn