Answer Choice D Company 2 is greater in avg rate of change by $750
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Explanation:
Average rate of change is the same as slope through two points. The two points are the endpoints of the interval.
The x values we'll use is x = 0 and x = 12 since it constitutes the first 12 years (12-0 = 12)
For company 1, if x = 0 and x = 12, then y = 12000 and y = 30000 respectively. The two points (0,12000) and (12,30000) are on the graph for company 1 The slope of the line through these two points is m = (y2-y1)/(x2-x1) m = (30000-12000)/(12-0) m = 18000/12 m = 1500 Over the first twelve years, the average rate of change for company 1 is 1500
For company 2, the points (0,15000) and (12,42000) are on the graph The slope of the line through these two points is m = (y2-y1)/(x2-x1) m = (42000-15000)/(12-0) m = (27000)/(12) m = 2250 Over the first twelve years, the average rate of change for company 2 is 2250
Now find the difference in the slopes 2250-1500 = 750
Company 2's rate of change is larger by $750 So that's why the answer is choice D. Over this timespan, company 2 is growing faster on average compared to company 1
