Natural gas and fracking gas wells using fracking of shale-gas source rocks produce half of their potential natural gas in the first year. another 25% is produced in year 2, and the decline continues downward at the same rate. in year 1, the typical barnet gas well produces 1 billion cubic feet of natural gas. the dallas region (barnett shale) had an initial surge in shale-gas wells peaking at about 1000 wells per year, then a slow tapering as the prime targets were gone and lesser targets were left. assume that year 1 had 1000 new wells, year 2 had another 950, year 3 another 900 – a slow drop of 50 wells per year through year 15. using time in years on the x-axis and total annual production (in tcf) on the y-axis, plot the annual production of natural gas from the assemblage of wells at the end of each of those 15 years. use totals at end of each year assuming the first 1000 wells drilled in year 1 had a full year of production equal to 1 billion cu ft (bcf) each. then these wells had the standard rate-of-decline as given above. in what year was the "peak" natural gas production? write your answers as a narrative instead of in scientific notation, ie, $20 million instead of $2.0x106 . using excel is the best way to organize the data.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

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step-by-step explanation:

why? because i noticed a pattern. 60 120. those numbers without the zero, make the 6 times tables leaving your answer to be b since 6 times 4 is 24 and adding a zero making it 240.