3. A collection of dogs were measured and weighed producing the following table of data [2]:

Length (cm)
from nose to anus

Body Weight
(gm)

Surface Area
(cm2)

51

3390

2320

100

25930

9106

62

5350

3284

76

10150

5070

74

5450

3815

a. The first model examines Weight (w) as a function of the Length (u). Use Excel's Trendline with the Power law to find the best fit to the data for a model of the form:
w = auk
In your Lab report write the best fit coefficients, a and k, found by Excel. Show a plot of this best fit curve with the data. What are the appropriate units for the coefficient a? From a biological perspective, briefly explain why the coefficient k has the value it does when fitting the data.

b. Repeat the process in Part a. for the surface area data graphing the surface area (s) as a function of length (u). In this case the model satisfies the allometric model:

s = auk
where the coefficients a and k differ from Part a. What are the appropriate units for this coefficient a? Don't forget to include a biological explanation along with your graph of the curve and the data.

[2] J. Mazumdar (1989), An Introduction to Mathematical Physiology and Biology, Australian Mathematical Society Lecture Note Series,Cambridge University Press, Cambridge.