The graph below shows the rate of natural gas usage (in therms per day) in one household for a 30 - day period. Estimate the total number of therms used during this period. Use left endpoints and rectangles with widths of 3 days.
View graph at:
postimg.o rg/image/61nw3co3r/
I came up with ans 165.
it's ok. I got it now.
To estimate the total number of therms used during the 30-day period shown in the graph, we need to calculate the areas of the rectangles under the curve. Each rectangle corresponds to a 3-day period, and the height of each rectangle represents the rate of natural gas usage (in therms per day).
First, we can estimate the rectangle heights by taking the left endpoint value for each corresponding 3-day period.
Looking at the graph, we can see that the left endpoint values are approximately:
Day 1-3: 15 therms/day
Day 4-6: 11 therms/day
Day 7-9: 10 therms/day
Day 10-12: 8 therms/day
Day 13-15: 6 therms/day
Day 16-18: 11 therms/day
Day 19-21: 14 therms/day
Day 22-24: 15 therms/day
Day 25-27: 12 therms/day
Day 28-30: 10 therms/day
Now, we can calculate the area of each rectangle (width times height) and sum them up to estimate the total number of therms used during the 30-day period.
Area of Day 1-3 rectangle = 3 days * 15 therms/day = 45 therms
Area of Day 4-6 rectangle = 3 days * 11 therms/day = 33 therms
Area of Day 7-9 rectangle = 3 days * 10 therms/day = 30 therms
Area of Day 10-12 rectangle = 3 days * 8 therms/day = 24 therms
Area of Day 13-15 rectangle = 3 days * 6 therms/day = 18 therms
Area of Day 16-18 rectangle = 3 days * 11 therms/day = 33 therms
Area of Day 19-21 rectangle = 3 days * 14 therms/day = 42 therms
Area of Day 22-24 rectangle = 3 days * 15 therms/day = 45 therms
Area of Day 25-27 rectangle = 3 days * 12 therms/day = 36 therms
Area of Day 28-30 rectangle = 3 days * 10 therms/day = 30 therms
Summing up all the rectangle areas, we get:
Total estimated therms used = 45 + 33 + 30 + 24 + 18 + 33 + 42 + 45 + 36 + 30 = 336 therms.
Therefore, the estimated total number of therms used during the 30-day period shown in the graph is 336 therms.