A town’s population was tracked over a period of 60 years. The results are shown on a scatterplot. From which data set was the scatterplot created?
Seven points are plotted on the coordinate plane.The horizontal axis is labeled Year, has a step size of 2.5, and displays the integers 0, 10, 20, 30, 40, 50, 60, and 70. The vertical axis is labeled Population, has a step size of 2,500, and displays the integers 0, 10,000, 20,000, 30,000, 40,000, 50,000, and 60,000. The following points are plotted: left parenthesis 0 comma 50,000 right parenthesis, left parenthesis 10 comma 30,000 right parenthesis, left parenthesis 20 comma 17,000 right parenthesis, left parenthesis 30 comma 9,000 right parenthesis, left parenthesis 40 comma 10,000 right parenthesis, left parenthesis 50 comma 11,200 right parenthesis, and left parenthesis 60 comma 12,500 right parenthesis. The points appear to lie on a curve that decreases to a minimum y value of 9,000 when x equals 30 and then decreases. The curve that the points would appear to lie on is concave up.
(1 point)
Responses
Year Population
0 50,000
10 30,000
20 17,000
30 9,000
40 5,000
50 3,000
60 1,900
Year Population 0 50,000 10 30,000 20 17,000 30 9,000 40 5,000 50 3,000 60 1,900
Year Population
0 50,000
10 30,000
20 17,000
30 9,000
40 10,000
50 11,200
60 12,500
Year Population 0 50,000 10 30,000 20 17,000 30 9,000 40 10,000 50 11,200 60 12,500
Year Population
0 1,900
10 3,000
20 5,000
30 9,000
40 17,000
50 30,000
60 50,000
Year Population 0 1,900 10 3,000 20 5,000 30 9,000 40 17,000 50 30,000 60 50,000
Year Population
0 17,000
10 30,000
20 50,000
30 12,500
40 11,200
50 10,000
60 9,000
Year Population 0 17,000 10 30,000 20 50,000 30 12,500 40 11,200 50 10,000 60 9,000
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1 answer
To determine which data set corresponds to the scatterplot described, we need to look closely at the plotted points and the overall trend exhibited in the graph.
The points given in the scatterplot are:
(0, 50,000)
(10, 30,000)
(20, 17,000)
(30, 9,000)
(40, 10,000)
(50, 11,200)
(60, 12,500)
From the description:
The population starts at 50,000 in year 0.
It decreases significantly to 30,000 in year 10, and further drops to a minimum of 9,000 in year 30.
After year 30, the population increases gradually to 12,500 by year 60.
Now, examining the options provided:
First option:
Year 0: 50,000
Year 10: 30,000
Year 20: 17,000
Year 30: 9,000
Year 40: 5,000
Year 50: 3,000
Year 60: 1,900
This option shows continuous decline without an increase after year 30, which does not match.
Second option:
Year 0: 50,000
Year 10: 30,000
Year 20: 17,000
Year 30: 9,000
Year 40: 10,000
Year 50: 11,200
Year 60: 12,500
This matches the pattern described in the scatterplot, with an initial decrease followed by an increase after year 30.
Third option:
Year 0: 1,900
Year 10: 3,000
Year 20: 5,000
Year 30: 9,000
Year 40: 17,000
Year 50: 30,000
Year 60: 50,000
This does not match since it starts much lower and does not fit the scatterplot trends.
Fourth option:
Year 0: 17,000
Year 10: 30,000
Year 20: 50,000
Year 30: 12,500
Year 40: 11,200
Year 50: 10,000
Year 60: 9,000
This also does not match the population trajectory in the scatterplot.
Based on this analysis, the correct data set from which the scatterplot was created is the second option:
