The women’s recommended weight formula from Harvard Pilgrim Healthcare says, "Give yourself 100 lb for the first 5 ft plus 5 lb for every inch over 5 ft tall."
a. Find a mathematical model for this relationship, where W be the recommended weight in lbs for a woman i inches over 5 ft tall.
W=______
b. Specify a reasonable domain and range for the function and then graph the function.
Domain: O less than or equal to i less than or equal to 15;
Range: 100 less than or equal to W less than or equal to _____
c. Use your model to calculate the recommended weight for
a woman of 5 feet, 6 inches
_____lbs
a woman of 5 feet, 8 inches
____lbs
a woman of 5 ft, 6 inches
130lbs....
a woman of 5 ft, 8 inches
140 lbs....
100 less than or equal to W less than or equal to 175
a. To find a mathematical model for this relationship, we can start by stating the given formula: "Give yourself 100 lb for the first 5 ft plus 5 lb for every inch over 5 ft tall." Let's break it down:
For the first 5 ft, which is 60 inches, the recommended weight is 100 lb.
For every inch over 5 ft tall, the recommended weight increases by 5 lb.
Using this information, we can form the mathematical model as follows:
W = 100 + 5(i - 60)
b. The domain represents the possible values for the input variable, which in this case is the number of inches (i) over 5 ft tall. Since the formula specifies the first 5 ft, we can consider a reasonable domain to be from 0 to 15 inches (inclusive). Therefore:
Domain: 0 ≤ i ≤ 15
The range represents the possible values for the output variable, which in this case is the recommended weight (W) in pounds. According to the formula, the recommended weight starts from 100 lb for a woman who is exactly 5 ft (60 inches) tall. It increases by 5 lb for every inch over 5 ft tall. Hence, a reasonable range would be:
Range: 100 ≤ W ≤ (100 + 5(15 - 60)), which simplifies to:
Range: 100 ≤ W ≤ 175
To graph this function, plot points for various values of i within the specified domain and connect them to form a line. The x-axis represents i (inches over 5 ft), and the y-axis represents the recommended weight in pounds (W).
c. Let's use the model to calculate the recommended weight for a woman of:
- 5 feet, 6 inches (66 inches):
W = 100 + 5(66 - 60)
W = 100 + 5(6)
W = 100 + 30
W = 130 lbs
- 5 feet, 8 inches (68 inches):
W = 100 + 5(68 - 60)
W = 100 + 5(8)
W = 100 + 40
W = 140 lbs
Therefore, a woman of 5 feet, 6 inches has a recommended weight of 130 lbs, and a woman of 5 feet, 8 inches has a recommended weight of 140 lbs.