1 / 20

CHAPTER 1

CHAPTER 1. Problem Solving and Critical Thinking. 1.2. Estimation, Graphs and Mathematical Models. Objectives. Use estimation techniques to arrive at an approximate answer to a problem. Apply estimation techniques to information given by graphs.

kameko-mack
Télécharger la présentation

CHAPTER 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 1 Problem Solving and Critical Thinking

  2. 1.2 Estimation, Graphs and Mathematical Models

  3. Objectives Use estimation techniques to arrive at an approximate answer to a problem. Apply estimation techniques to information given by graphs. Develop mathematical models that estimate relationships between variables.

  4. Estimation The process of arriving at an approximate answer to a question. Methods of Estimation • Rounding Numbers • Using Graphs • Using Mathematical Models

  5. Rounding Whole Numbers • The symbol ≈ means “is approximately equal to”

  6. Example 1: Rounding A Whole Number • Round the World population 6,751,593,103 • To the nearest million: • To the nearest thousand:

  7. Example 2: Rounding The Decimal Part of a Number • The first seven digits of π are: 3.141592. Round π: • To the nearest hundredth: 3.141592 • To the nearest thousand: 3.141592.

  8. Example 3: Estimation by Rounding • You purchased bread for $2.59, detergent for $2.17, a sandwich for $3.65, an apple for $0.47 and coffee for $5.79. The total bill was $18.67. Is this amount reasonable? • To check, round the cost of each item to the nearest dollar. • This bill of $18.67 seems high compared to the $15.00 estimate.

  9. Use a circle to represent the whole and divide it into sectors proportional to their part of the whole. According to the U.S. Census Bureau, in 2008, there were 220,948,915 Americans 20 years and older. Assuming the circle graph is representative of this age group, a. Determine a calculation that shows the number of Americans 20 years and older who define old age by a decline in physical ability. b. Use rounding to find a reasonable estimate. Example 5: Applying Estimation Techniques to a Circle Graph

  10. Example 5 continued b. Estimate the Answer Approximately 88 million Americans 20 years and older define old age by a decline in physical ability. a. Compute the exact answer

  11. Estimation with Graphs: Bar Graphs • Bar graphs use a vertical or horizontal bar to represent each item. • The length of the bar determines the amount. • We can use bar graphs to make predictions.

  12. Example 6: Applying Estimation and Inductive Reasoning to Data in a Bar Graph a. Estimate a man’s increased life expectancy, rounded to the nearest hundredth of a year, for each future birth year. For each subsequent birth year, a man’s life expectancy is increasing by approximately 0.19 year.

  13. Example 6: Applying Estimation and Inductive Reasoning to Data in a Bar Graph continued b. Estimate the life expectancy of a man born in 2020. An American man born in 2020 will have a life expectancy of approximately 78 years.

  14. Estimation with Graphs: Line Graphs • Line graphs illustrate trends over time • Horizontal axis represents time • Vertical axis represents the age

  15. Example 7: Using a Line Graph • Find an estimate for the percentage of seniors who used marijuana in 1990. In 1990, approximately 14% of seniors used marijuana.

  16. Example 7: Using a Line Graph continued In which five-year period did the percentage of seniors who used marijuana decrease at the greatest rate? The percentage of seniors using marijuana decreased at the greatest rate in the five-year period from 1985 through 1990.

  17. Estimation with Mathematical Models • The process of finding formulas to describe real-world phenomena.

  18. Example 8: Modeling the Cost of Attending a Public College a. Estimate the yearly increase in tuition and fees. The average yearly increase is about $353.

  19. Example 8: continued b. Obtain a mathematical model that estimates the average cost of tuition and fees, for the school year ending x years after 2000.

  20. Example 8 continued c. Use the mathematical model to project the average cost of tuition and fees for the school year ending in 2014. • The model projects that the average cost of tuition and fees for the school year ending in 2014 will be $8304.

More Related