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 $f(1900) = 165$
what are the units of 1900? ? 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 $f'(2000)=0$,
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 $f^{-1}(170) = 2500$,
what are the units of 170? ? lb cal day lb/cal cal/lb cal/day lb/day day/lb day/cal
what are the units of 2500? ? 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 2700 to 2740 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.
$f'\Big($ $\Big)=$