The Size of a Horse
Consider this formula: f(W) = (0.1)W^{2/3}
Animal physiologists claim that this formula determines the surface area of a horse (m^{2}) as a function of its weight (kgs).
Also, suppose you can't get a horse to balance on a bathroom scale. The "cowboy's ruleofthumb" is to use this formula:
Weight {[(Heart girth)^{2} x length]/300} + 50
where the heart girth and length are measured in inches, producing a weight in pounds.
Task 1: How can you adjust the constant of 0.1 in the first formula so that computations can be made in English units and not metric units?
Task 2: How would you gather data to check on the validity of both of these formulas?
Note: In case you are curious (and you are), Tabler's Cyclopedic Medical Dictionary (1993) claims you can calculate the surface area of human skin by this formula:
S.A. = (0.007184)(your weight in kgs)^{0.425}(your height in cms)^{0.725}
Source: K. Kalmanson & P. Lenschaft's Mathematics: A Practical Approach, 1978, p. 41
