Question

marge is trying to lose weight. her diet resulted in losing 3 pounds over 3 weeks. then, she added exercise to her schedule and lost 6 pounds in 2 weeks. which graph shows how exercise affected marges weight?

Explanation:

Step1: Calculate rate before exercise

Marge lost 3 pounds in 3 weeks. The rate is $\frac{3}{3} = 1$ pound per week. So in 3 weeks, she loses 3 pounds (since 1*3 = 3).

Step2: Calculate rate after exercise

After adding exercise, she lost 6 pounds in 2 weeks. The rate is $\frac{6}{2} = 3$ pounds per week. So after 3 weeks (when she starts exercising), in the next 2 weeks (total 3 + 2 = 5 weeks), the weight loss should increase more steeply.

Step3: Analyze the graphs

• Graph A: The first segment (before exercise) has a steeper slope (losing weight faster initially) which is wrong because initial rate was 1 lb/week.
• Graph B: The first segment (0 - 3 weeks) has a slope of 1 (losing 3 pounds in 3 weeks), then the second segment (after 3 weeks) has a steeper slope (since 3 lb/week is steeper than 1 lb/week), which matches our calculation.

Answer:

B