The graph for Exercise is plotted on a logarithmic scale

Chapter 2, Problem 86A

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Problem 86A

The graph for Exercise is plotted on a logarithmic scale where differences between successive measurements are not always the same. Data that do not plot in a linear pattern on the usual Cartesian axes often form a linear pattern when plotted on a logarithmic scale. Notice that on the horizontal scale, the distance from 5 to 10 is not the same as the distance from 10 to 15, and so on. This is characteristic of a graph drawn on logarithmic scales.

Metabolism Rate The accompanying graph shows the basal metabolism rate (in cm3 of oxygen per gram per hour) for marsupial carnivores, which include the Tasmanian devil. This rate is inversely proportional to body mass raised to the power 0.25. Source: The Quarterly Review of Biology.

a. Estimate the metabolism rate for a marsupial carnivore with body mass of 10 g. Do the same for one with body mass of 1000 g.

b. Verify that if the relationship between x and y is of the form y = axb, then there will be a linear relationship between ln x and ln y. (Hint: Apply ln to both sides of y = axb.)

c. If a function of the form y = axb contains the points (x1, y1) and (x2, y2), then values for a and b can be found by dividing  by , solving the resulting equation for b, and putting the result back into either equation to solve for a. Use this procedure and the results from part a to find an equation of the form y = axb that gives the basal metabolism rate as a function of body mass.

d. Use the result of part c to predict the basal metabolism rate of a marsupial carnivore whose body mass is 100 g.