2. In this problem use the power rule to determine the pulse (beats per min) as a function of the weight (kg) of the animal. You are given the following data concerning six animals [1]:

a. Let P be the pulse and w be the weight, then the power law expression relating the pulse to the weight is given by

Use the power law under Excel's trendline to best fit the data above. Plot the data and the best power law fit and have Excel write the formula on your graph. (Note that you will be adding the model from Part c to this graph, so wait to enter only one graph in your Lab report.)

b. Determine the sum of squares error between the data and the model that you found in Part a. How well does the graph match the data? Find the percent error between the pulse given by the model and the actual data for each of the animals in the table above. (Assume that the weight in the table is accurate.) Which animal has the highest percent error and explain why you might expect this? Also, which animal has the lowest percent error and explain why this might be the case?

c. Use the applet below to find the nonlinear least squares best fit to the data. (There is a hyperlink in the allometric section discussing this nonlinear fit.) Minimize the sum of squares error, then write in your lab report the equation of the best model and the value for the sum of squares error. Find the percent error between the pulse given by this model and the actual data for each of the animals in the table above. Simulate this model and add its graph to the graph produced in Part a. Compare this model to the one given by Excel above. Which is the better model? Explain why differences arise.

e. Write an expression for the derivative P '(w) for each of the models. Is the function increasing, decreasing, or neither? Write a brief paragraph that describes how pulse and weight are related based on these models.