1.2 Estimation Techniques 13 each of which is the length of the segment shown on the scale. You should obtain approximately 4 intervals. Thus, the distance is about 4 250 × mi, or about 1000 mi. b) Using the procedure discussed in part (a), we estimate that on the map there are about 2.2 intervals, each of which is the length of the segment shown on the scale. Thus, the distance from Fort Hall to Sacramento, is about 2.2 250 mi, × or about 550 mi. 7 Now try Exercise 37 Example 6 Estimated Energy Use Some utility bills contain graphs illustrating the amount of electricity and natural gas used. The following graphs show gas and electric use at a specific residence for a period of 13 months, starting in November 2023 and going through November 2024 (the month of the current bill). Also shown is the bill for the average residential customer for November 2024. Using these graphs, answer the following questions. Gas Use (therms) N D M O J F A A M J J S N A V G Electric Use (kWh) 240 200 160 120 80 40 2023 2024 N D M O J F A A M J J S N A V G 2023 Month Month 2024 0 Actual use Estimated use Average customer use 2400 2000 1600 1200 800 400 0 a) How often were actual gas and electric readings made? b) Estimate the number of therms of gas used by the average residential customer in November 2024. c) Estimate the amount of gas used by the resident in November 2024. d) If the cost of gas is $1.12295 per therm, estimate the gas bill in March 2024. e) In which month was the most electricity used? How many kilowatt-hours (kWh) of electricity were used in this month? f) If the cost of electricity is 10.0127 cents per kWh, estimate the cost of the electricity in January 2024. Solution a) Actual readings were made every other month, in November 2023, January 2024, March 2024, May 2024, July 2024, September 2024, and November 2024. Thus, actual readings were made 7 times. b) In November 2024, approximately 75 therms were used by the average residential customer, as shown by the height of the bar on the far right. c) In November 2024, approximately 60 therms were used by the resident. d) In March 2024, about 180 therms were used. The rate is $1.12295 per therm. To get a rough approximation, round the rate to $1.12 per therm. 1.12 180 $201.60 × = Thus, the cost of gas used was about $201.60. Did You Know? Early Estimation The ancient Egyptians and Greeks used sticks to estimate heights. To measure height, a person held out a stick until it just covered the height of the object. The person then turned the stick through a right angle. Measuring the distance the stick appeared to cover on the ground provided an estimate of the object’s height.
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