Question
With aging, body fat increases and muscle mass declines. The graph to the right shows the percent body fat in a group of adult women and men as they age from 25 to 75 years. Age is represented along the x-axis, and percent body fat is represented along the y-axis. State the intervals on which the graph giving the percent body fat in women is increasing and decreasing.
Percent Body Fat in Adults
25
50
75
20
30
40
Age
Percent Body Fat
Men
Women
A graph titled "Percent Body Fat in Adults" has a horizontal axis labeled "Age" from 25 to 75 in increments of 5 and a vertical axis labeled "Percent Body Fat" from 20 to 40 in increments of 2. The graph consists of two plots of points. The first plot labeled "Women" consists of six plotted points connected by line segments from left to right. The coordinates of the plotted points are (25, 32), (35, 34.2), (45, 40), (55, 37), (65, 35), and (75, 32). The second plot labeled "Men" consists of six plotted points connected by line segments from left to right. The coordinates of the plotted points are (25, 20), (35, 28), (45, 25), (55, 24), (65, 23), and (75, 20).
Question content area bottom
Part 1
On what interval is the graph increasing?
A.left parenthesis 25 comma 75 right parenthesis
left parenthesis 25 comma 75 right parenthesis
B.left parenthesis 20 comma 28 right parenthesis
left parenthesis 20 comma 28 right parenthesis
C.left parenthesis 45 comma 75 right parenthesis
left parenthesis 45 comma 75 right parenthesis
D.left parenthesis 25 comma 45 right parenthesis
left parenthesis 25 comma 45 right parenthesis
Percent Body Fat in Adults
25
50
75
20
30
40
Age
Percent Body Fat
Men
Women
A graph titled "Percent Body Fat in Adults" has a horizontal axis labeled "Age" from 25 to 75 in increments of 5 and a vertical axis labeled "Percent Body Fat" from 20 to 40 in increments of 2. The graph consists of two plots of points. The first plot labeled "Women" consists of six plotted points connected by line segments from left to right. The coordinates of the plotted points are (25, 32), (35, 34.2), (45, 40), (55, 37), (65, 35), and (75, 32). The second plot labeled "Men" consists of six plotted points connected by line segments from left to right. The coordinates of the plotted points are (25, 20), (35, 28), (45, 25), (55, 24), (65, 23), and (75, 20).
Question content area bottom
Part 1
On what interval is the graph increasing?
A.left parenthesis 25 comma 75 right parenthesis
left parenthesis 25 comma 75 right parenthesis
B.left parenthesis 20 comma 28 right parenthesis
left parenthesis 20 comma 28 right parenthesis
C.left parenthesis 45 comma 75 right parenthesis
left parenthesis 45 comma 75 right parenthesis
D.left parenthesis 25 comma 45 right parenthesis
left parenthesis 25 comma 45 right parenthesis
Answers
Answered by
GPT-4o mini
To determine the intervals on which the graph giving the percent body fat in women is increasing, we look at the coordinates provided:
- (25, 32)
- (35, 34.2)
- (45, 40)
- (55, 37)
- (65, 35)
- (75, 32)
We analyze the changes in percent body fat as age increases:
1. From age 25 to 35: percent body fat increases from 32 to 34.2 (increasing).
2. From age 35 to 45: percent body fat increases from 34.2 to 40 (increasing).
3. From age 45 to 55: percent body fat decreases from 40 to 37 (decreasing).
4. From age 55 to 65: percent body fat decreases from 37 to 35 (decreasing).
5. From age 65 to 75: percent body fat decreases from 35 to 32 (decreasing).
Based on this analysis, we conclude that the percent body fat in women is increasing in the ranges:
- From age 25 to 35.
- From age 35 to 45.
Thus, the overall interval where the graph is increasing is:
**D. (25, 45)**
- (25, 32)
- (35, 34.2)
- (45, 40)
- (55, 37)
- (65, 35)
- (75, 32)
We analyze the changes in percent body fat as age increases:
1. From age 25 to 35: percent body fat increases from 32 to 34.2 (increasing).
2. From age 35 to 45: percent body fat increases from 34.2 to 40 (increasing).
3. From age 45 to 55: percent body fat decreases from 40 to 37 (decreasing).
4. From age 55 to 65: percent body fat decreases from 37 to 35 (decreasing).
5. From age 65 to 75: percent body fat decreases from 35 to 32 (decreasing).
Based on this analysis, we conclude that the percent body fat in women is increasing in the ranges:
- From age 25 to 35.
- From age 35 to 45.
Thus, the overall interval where the graph is increasing is:
**D. (25, 45)**