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Estimation, Graphs, and Mathematical Models

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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.

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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.

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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 $20 in your wallet and you don’t want to be caught in the checkout line without enough money. Use rounding to the nearest ten cents to: a. Estimate the total cost of your purchases. b. Decide if it is safe to put the ice cream in your cart. Item Cost ($) Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid 2.87 TOTAL:

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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 = 6. Then add the cents to get = 70 cents, so the total is $6.70. You can easily add in the other numbers one at a time to get the total. Doing this kind of mental arithmetic will make you a stronger mathematics student. ItemCost ($) Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid2.87 TOTAL:

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ItemCost ($) Cost Rounded to Nearest Ten cents Cereal4.29 Milk2.41 Bread1.89 Lunch Meat3.36 Pickles2.47 Dish-washing liquid 2.87 TOTALS:

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A carpenter who works full time earns $28 per hour. a. Estimate the carpenter’s weekly salary. b. Estimate the carpenter’s annual salary.

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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.

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Marc is buying 19 blank tapes at $2.89 each. Use compatible numbers to estimate the cost of the tapes.

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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?

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The bar graph shows the average cost of tuition and fees for public four-year colleges, adjusted for inflation.

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Estimate the yearly increase in tuition and fees. Round to the nearest dollar.

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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.

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Use the mathematical model to predict the tuition and fees for the school year ending in 2014.

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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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