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Section 1.2

Estimation, Graphs, and Mathematical Models. Section 1.2. 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. Key Term.

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Section 1.2

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  1. Estimation, Graphs, and Mathematical Models Section 1.2

  2. 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.

  3. Key Term • Estimation: the process of arriving at an approximate answer to a question. • For example, companies estimate the amount of their products consumers are likely to use, and economists estimate financial trends. • Rounding numbers is also an estimation method.

  4. Example 1: Rounding • On your way home from work, you stopped at the market to pick up the items listed in the Table. You also would like to buy a half gallon of ice cream for $3.59, but you remember that you only have $20 in your wallet and you don’t want to be caught in the checkout line without enough money. Use rounding to the nearest ten cents to: • Estimate the total cost of your purchases. • Decide if it is safe to put the ice cream in your cart.

  5. Food for thought… • You do not need a calculator to add the estimated prices. For example to add $4.30 and $2.40, first add the dollars to get 2 + 4 = 6. Then add the cents to get 30 + 40 = 70 cents, so the total is $6.70. You can easily add in the other numbers one at a time to get the total. Doing this kind of mental arithmetic will make you a stronger mathematics student.

  6. Table

  7. Example 2: • A carpenter who works full time earns $28 per hour. • Estimate the carpenter’s weekly salary. • Estimate the carpenter’s annual salary.

  8. Using compatible numbers • Another way to make a quick estimate that is slightly different from rounding is to use compatible numbers. • When compatible numbers, instead of the numbers given in the problems, you simply substitute numbers that are easier to work with. • For example, instead of dividing 298 by 14, you could divide 300 by 15 to get 20. • Or, instead of multiplying 11 times 73, you could multiply 73 by 10 to get 730.

  9. Example 3:Compatible Numbers • Marc is buying 19 blank tapes at $2.89 each. Use compatible numbers to estimate the cost of the tapes.

  10. Example 4:Compatible Numbers • In 2001, the world’s population was approximately 6,157 million and the population of North America was 486 million. Estimate what fractional part of the world’s population lives in North America?

  11. Example 5:Interpreting Graphical Data • The bar graph shows the average cost of tuition and fees for public four-year colleges, adjusted for inflation.

  12. Example 5:Interpreting Graphical Data • Estimate the yearly increase in tuition and fees. Round to the nearest dollar.

  13. Example 5:Interpreting Graphical Data • Write a mathematical model that estimates the average cost of tuition and fees, T, at public four-year colleges for the school year ending x years after 2000.

  14. Example 5:Interpreting Graphical Data • Use the mathematical model to predict the tuition and fees for the school year ending in 2014.

  15. Section 1.2 Assignments • Classwork: • TB pg. 21/20 – 42 Even • Must write problem and show ALL work to receive credit for the assignment. • Homework:

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