12 CHAPTER 1 Critical Thinking Skills Round these numbers to obtain an estimate. 1300 50 26 = Therefore, the car averaged about 26 miles per gallon. c) To estimate the total cost of gasoline, multiply the price per gallon by the number of gallons of gasoline used. 52 $3.95 × Round these numbers and multiply to obtain an estimate. 50 $4 $200 × = Thus, the cost of gasoline is about $200. 7 Now try Exercise 31 Example 5 Estimating Distances on Trails to the West In the mid-1800s, thousands of settler-colonizers followed trails to the West. One of the main trails to the West was the Oregon Trail, which ran from Independence, Missouri, to the Oregon Territory. Another trail, the California Trail, ran from Fort Hall on the Oregon Trail to Sacramento, California. Following is a map of the Oregon Trail and the California Trail. PACIFIC OCEAN Oregon Trail California Trail OREGON TERRITORY NEW MEXICO TERRITORY UTAH TERRITORY UNORGANIZED TERRITORY TEXAS Ft. Hall San Francisco Independence Missouri Chimney Rock Great Plains Sierra Nevada 250 Miles 0 Cascade Range Trails to the West, 1850 CALIFORNIA Sacramento ROCKY MOUNTAINS South Pass Sublette Cutoff a) Using the scale shown and the Oregon Trail, estimate the distance from Independence, Missouri, to Fort Hall in the Oregon Territory. b) Using the scale shown and the California Trail, estimate the distance from Fort Hall in the Oregon Territory to Sacramento, California. Solution a) The segment shown on the scale of the map represents 250 miles (mi). We can determine the distance from Independence to Fort Hall by marking off intervals Now let’s look at some different types of estimation problems. MATHEMATICS TODAY Estimating Techniques in Medicine Estimating is one of the diagnostic tools used by the medical profession. Physicians take a small sample of blood, tissue, or body fluids to be representative of the body as a whole. Human blood contains different types of white blood cells that fight infection. When a bacterium or virus gets into the blood, the body responds by producing more of the type of white blood cell whose job it is to destroy that particular invader. Thus, an increased level of white blood cells in a sample of blood not only indicates the presence of an infection but also helps identify its type. A trained medical technician estimates the relative number of each kind of white blood cell found in a count of 100 white blood cells. An increase in any one kind indicates the type of infection present. Why This Is Important By using estimation techniques, healthcare professionals can more accurately determine the type and severity of the illness present in a patient. Knowing this information may help select an appropriate course of treatment that will improve the health of the patient. Eosinophils (wbc) Neutrophil (wbc) Monocyte (wbc) Red blood cells m A high count of eosinophils (a particular kind of white blood cell, or wbc) can be an indicator of an allergic reaction.
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