Presentation is loading. Please wait.

Presentation is loading. Please wait.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 296 Tell whether the function is an exponential.

Similar presentations


Presentation on theme: "Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 296 Tell whether the function is an exponential."— Presentation transcript:

1 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.

2 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.

3 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.

4 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.

5 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.

6 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.

7 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.

8 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.

9 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 9 Homework, Page 296 29. 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?

10 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 10 Homework, Page 296 29. 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?

11 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 11 Homework, Page 296 33. 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.

12 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 12 Homework, Page 296 37. Using the population model that is graphed, explain why the time it takes the population to double is independent of the population size.

13 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 13 Homework, Page 296 41. Determine the atmospheric pressure outside an aircraft flying at 52,800 ft (10 miles above sea level).

14 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 14 Homework, Page 296 45.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?

15 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 15 Homework, Page 296 45.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?

16 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 16 Homework, Page 296 53.What is the constant percentage growth rate of a.49% b.23% c.4.9% d.2.3% e.1.23%

17 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 17 Homework, Page 296 57.a. Use the data in the table and logistic regression to predict the population in 2000. The logistic model predicts a population of 281.1 million people in the year 2000. b. Compare the prediction with the value listed in the table for 2000. 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).

18 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.3 Logarithmic Functions and Their Graphs

19 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 19 Quick Review

20 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 20 Quick Review Solutions

21 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 21 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.

22 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 22 Changing Between Logarithmic and Exponential Form

23 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 23 Inverses of Exponential Functions

24 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 24 Basic Properties of Logarithms

25 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 25 Example Evaluating Logarithms Evaluate the logarithmic expression without using a calculator.

26 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 26 An Exponential Function and Its Inverse

27 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 27 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.

28 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 28 Basic Properties of Common Logarithms

29 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 29 Example Solving Simple Logarithmic Equations

30 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 30 Basic Properties of Natural Logarithms

31 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 31 Example Evaluating Natural Logarithms Evaluate the logarithmic expressions:

32 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 32 Graphs of the Common and Natural Logarithm

33 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 33 Example Drawing Logarithmic Graphs Draw the graph of the given function:

34 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 34 Example Transforming Logarithmic Graphs

35 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 35 Decibels

36 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 36 Example Computing Decibel Levels Compute the decibel levels of the following Subway train Threshold of pain

37 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 37 Homework Review Section 3.3 Page 308, Exercises: 1 – 65 (EOO), 59

38 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.4 Properties of Logarithmic Functions

39 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 39 Quick Review

40 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 40 Quick Review Solutions

41 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 41 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.

42 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 42 Properties of Logarithms

43 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 43 Example Proving the Product Rule for Logarithms

44 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 44 Example Expanding the Logarithm of a Product

45 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 45 Example Expanding the Logarithm of a Quotient

46 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 46 Example Condensing a Logarithmic Expression

47 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 47 Change-of-Base Formula for Logarithms

48 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 48 Example Evaluating Logarithms by Changing the Base

49 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 49 Example Graphing Logarithmic Functions

50 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 50 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 – 2000. Such a transformation is called a re-expression.

51 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 51 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) Mercury0.38700.2410 Venus0.72330.6161 Earth1.00000.0000 Mars1.5231.981 Jupiter5.20311.86 Saturn9.53929.46


Download ppt "Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 296 Tell whether the function is an exponential."

Similar presentations


Ads by Google