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

(a) In the statement $f(1600) = 155$
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 155? ? 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 $f'(2000)=0$,
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 $f^{-1}(164) = 2100$,
what are the units of 164? ? lb cal day lb/cal cal/lb cal/day lb/day day/lb day/cal
what are the units of 2100? ? 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 $f'(c)=dW/dc$? ? 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 3000 to 3020 calories per day, then her weight will increase by approximately 0.3 pounds.
Fill in the blanks below so that the equation supports her conclusion.
$f'\Big($ $\Big)=$