A laboratory study investigating the relationship between diet and weight in adult humans found that the weight of a subject, \(W\text{,}\) in pounds, was a function, \(W=f(c)\text{,}\) of the average number of Calories, \(c\text{,}\) consumed by the subject in a day.

*(a)* In the statement \(f(1600) = 165\)

what are the units of 1600?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

what are the units of 165?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

*(Think about what this statement means in terms of the weight of the subject and the number of calories that the subject consumes.)*

*(b)* In the statement \(f'(2000)=0\text{,}\)

what are the units of 2000?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

what are the units of 0?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

*(Think about what this statement means in terms of the weight of the subject and the number of calories that the subject consumes.)*

*(c)* In the statement \(f^{-1}(173) = 2400\text{,}\)

what are the units of 173?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

what are the units of 2400?

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

*(Think about what this statement means in terms of the weight of the subject and the number of calories that the subject consumes.)*

*(d)* What are the units of \(f'(c)=dW/dc\text{?}\)

lb

cal

day

lb/cal

cal/lb

cal/day

lb/day

day/lb

day/cal

*(e)* Suppose that Sam reads about \(f'\) in this study and draws the following conclusion: If Sam increases her average calorie intake from 2800 to 2840 calories per day, then her weight will increase by approximately 0.8 pounds.

Fill in the blanks below so that the equation supports her conclusion.

\(f'\Big(\) \(\Big)=\)