Question

beths tomato plants were producing 10 tomatoes a week. then, it stopped raining. since then, she has only grown 5 tomatoes in 7 weeks. which graph shows how the rain affected beths tomatoes?

Explanation:

Step1: Analyze initial production

Beth's tomato plants initially produced 10 tomatoes per week. So, for the first part (before it stopped raining), the number of tomatoes produced should increase at a rate of 10 per week.

Step2: Analyze production after rain stopped

After it stopped raining, she grew 5 tomatoes in 7 weeks. The rate here is $\frac{5}{7}$ tomatoes per week, which is much slower than 10 per week.

Step3: Compare graphs

- Graph A: The first segment (red) has a very steep slope (high rate, like 10 per week initially) and then the blue segment has a less steep slope (lower rate, like $\frac{5}{7}$ per week). But wait, initially, before the rain stopped, the production was 10 per week. Wait, maybe I misread. Wait, the problem says "Beth's tomato plants were producing 10 tomatoes a week. Then, it stopped raining. Since then, she has only grown 5 tomatoes in 7 weeks." So before the rain stopped, the rate was 10 tomatoes per week. After, it's 5/7 per week.
- Graph B: The red segment has a slope of 10/5 = 2 tomatoes per week (since it goes from 0 to 10 in 5 weeks), which is not 10 per week. Wait, maybe the x - axis is weeks. Let's re - examine.
Wait, maybe the first part (before rain stopped) is a steeper line (higher rate) and the second part (after rain stopped) is a less steep line (lower rate). Let's calculate the rate for each part of the graphs.
For Graph A: The red part: from week 0 to week 1 (approx), it goes from 0 to 20? No, wait the y - axis is tomatoes produced. Wait, maybe the initial production (before rain stopped) is a steeper line (10 per week) and after (5 in 7 weeks, so slow). Graph B: The red line goes from 0 to 10 in 5 weeks (rate 2 per week), which is not 10. Graph A: The red line goes from 0 to 20 in 1 week? No, maybe I misinterpret. Wait, the key is: before rain stopped, rate = 10 tomatoes/week. After, rate = 5 tomatoes/7 weeks≈0.714 tomatoes/week.
So the first segment (before rain) should have a steep slope (high rate) and the second (after) a shallow slope (low rate). Graph A has a steep first segment (red) and a less steep second (blue). Graph B has a less steep first (red) and a steeper second (blue), which is the opposite. So Graph A is incorrect, Graph B? Wait no, wait the problem says "which graph shows how the rain affected Beth's tomatoes". Wait, maybe I got the time when the rain stopped wrong. Maybe the first part is before rain stopped (high rate) and the second part is after (low rate). So the graph should have a steep line first (high rate) and then a shallow line (low rate). Let's check the slopes:
- Graph A: Red line: from (0,0) to (1,20) (approx), slope = 20/1 = 20 (too high, but maybe the scale is different). Wait, no, the y - axis is up to 25. Wait, maybe the initial production (before rain stopped) is 10 per week, so in 1 week, 10 tomatoes. So the red line in Graph A: from (0,0) to (1,10) (if the x - axis is weeks). Wait, maybe the x - axis is weeks. Let's look at the x - axis labels: weeks from 0 to 9.
Graph A: Red line: from (0,0) to (1,20)? No, the y - axis is tomatoes produced. Wait, maybe the first part (before rain stopped) is a steeper line (higher rate) and the second (after) is a less steep line (lower rate). Graph B: Red line: from (0,0) to (5,10), slope = 10/5 = 2 tomatoes per week (not 10). Graph A: Red line: from (0,0) to (1,20), slope = 20/1 = 20 (too high). Wait, maybe I made a mistake. Wait the problem says "Beth's tomato plants were producing 10 tomatoes a week. Then, it stopped raining. Since then, she has only grown 5 tomatoes in 7 weeks." So before rain stopped, rate r1 = 10 tomatoes/week. After, rate r2 = 5/7 tomatoes/week. So r1 > r2. So the graph should have a steeper slope (higher rate) first and then a shallower slope (lower rate) after the rain stopped.
Looking at the two graphs:
- Graph A: The first segment (red) has a very steep slope (high rate) and the second (blue) has a less steep slope (low rate).
- Graph B: The first segment (red) has a less steep slope (low rate) and the second (blue) has a steeper slope (high rate), which is the opposite of what we need.
Wait, maybe the rain stopped at some point, say week 1 or week 5. Wait, in Graph B, the red line goes up to 10 tomatoes at week 5, then the blue line goes up. If before rain stopped (first 5 weeks), the rate was 10/5 = 2 tomatoes per week (not 10). In Graph A, the red line goes up to 20 tomatoes at week 1, then the blue line. If before rain stopped (first week), the rate was 20 tomatoes per week (not 10). Wait, maybe the problem is that the initial production (before rain stopped) is a steeper line (higher rate) and after (lower rate). So the correct graph should have a steeper line first and then a less steep line. So Graph A has a steeper first line (red) and a less steep second line (blue), which matches the rate change (high rate before rain, low rate after). Graph B has a less steep first line and a steeper second line, which is wrong. So the correct graph is A? Wait no, maybe I messed up. Wait the problem says "Beth's tomato plants were producing 10 tomatoes a week. Then, it stopped raining. Since then, she has only grown 5 tomatoes in 7 weeks." So before rain stopped, the number of tomatoes produced per week is 10, so the line should be steep (slope 10). After, slope is 5/7≈0.714. So the graph with a steep line first and then a shallow line is the correct one. So Graph A has a steep red line (high rate) and a shallow blue line (low rate), so Graph A is correct? Wait no, maybe the x - axis is weeks, and the first part (before rain) is a steeper line. So the answer should be Graph A? Wait, no, maybe I made a mistake. Wait let's re - calculate the rate for each graph's segments.
For Graph B: The red segment: from (0,0) to (5,10). The rate is 10 tomatoes / 5 weeks = 2 tomatoes per week. The blue segment: from (5,10) to (9,25). The number of tomatoes produced is 25 - 10 = 15 in 4 weeks, rate = 15/4 = 3.75 tomatoes per week.
For Graph A: The red segment: from (0,0) to (1,20). Rate = 20 tomatoes / 1 week = 20 tomatoes per week. The blue segment: from (1,20) to (9,25). Tomatoes produced = 5 in 8 weeks, rate = 5/8 = 0.625 tomatoes per week.
Wait, the initial rate was 10 tomatoes per week. The red segment in Graph A has a rate of 20, which is higher than 10, and the blue segment has a rate of 0.625, which is lower than 5/7≈0.714. The red segment in Graph B has a rate of 2, which is lower than 10, and the blue segment has a rate of 3.75, which is higher than 5/7. So neither is perfect, but Graph A's red segment is steeper (higher rate) and blue is shallower (lower rate), which is closer to the problem's description (high rate before rain, low rate after). So the correct graph is A.

Answer:

A