Question

A dog owner is told by the veterinarian that his dog, Max, is overweight and needs to lose 4 to 5 pounds in order to live a healthy life. The dog weighs 126 pounds when he is put on a special diet to aid in the weight loss. The vet predicts that the diet will allow Max to lose 4 ounces per week. Max is brought to the vet every 2 weeks for a weight check. Write an equation to represent the doctor's prediction, and the relationship between Max's weight in pounds, y, and the number of times Max's weight is checked, x, in periods of two weeks . Reduce all answers to the nearest tenth of a number.

Answer 1

This is a linear function, of the kind y = mx + b

where x is the number of visit,  b is the weight when x = 0, and m is the predicted change of weight for every visit.

m = - 4 ounces / visit, which must be converted to pounds (the negative sign indicates that the change is a decrease)

1 lb = 16 ounces = 4 ounces = 0.25 lb

Then m = - 0.25 lb / visit.

Now, for x = 1, y = 126 => 126 = - 0.25(1) + b => b = 126 + 0.25 = 126.25

Then the function is y = 126.25 - 0.25x

Now round to the nearest tenth:

y = 126.3 - 0.3x

Answer: y = 126.3 - 0.3x