The bar graph shows the estimated number of calories per day needed to maintain energy balance for various gender and age groups for moderately active lifestyles. (Moderately active means a lifestyle that includes physical activity equivalent to walking 1.5 to 3 miles per day at 3 to 4 miles per hour, in addition to the light physical activity associated with typical day-to-day life.)

a. The mathematical model W = -66x² + 526x + 1030 describes the number of calories needed per day, W, by women in age group x with moderately active lifestyles. According to the model, how many calories per day are needed by women between the ages of 19 and 30, inclusive, with this lifestyle? Does this underestimate or overestimate the number shown by the graph? By how much?

b. The mathematical model M = -120x² + 998x + 590 describes the number of calories needed per day, M, by men in age group x with moderately active lifestyles. According to the model, how many calories per day are needed by men between the ages of 19 and 30, inclusive, with this lifestyle? Does this underestimate or overestimate the number shown by the graph? By how much?

c. Write a simplified rational expression that describes the ratio of the number of calories needed per day by women in age group x to the number of calories needed per day by men in age group x for people with moderately active lifestyles.

Transcribed Image Text:

Calories per Day 3200 2800 2400 2000 1600 1200 800 400 Women Men Group 1 1500 1500 Calories Needed to Maintain Energy Balance for Moderately Active Lifestyles Group 3 Group 4 Group 5 4-8 Group 2 1800 2000 9-13 2000 2600 ***** 2100 2700 14-18 19-30 Age Range 2000 2500 Group 6 ...….... 1800 2300 31-50 51+