In a case study where the maximal rates of oxygen consumption (in ml/s) for nine species of wild African mammals were plotted against body mass (in kg) in a log-log plot, it was found that the data points fell on a straight line with the slope approximately equal to 0.3 and the vertical axis intercept of approximately 0.101. Find an equation that relates maximal oxygen consumption, r, and body mass, m.
To find the equation that relates maximal oxygen consumption (r) and body mass (m), we need to use the slope and vertical axis intercept values from the given information.
In a log-log plot, an equation of the form y = a * x^b represents a straight line, where y is the dependent variable, x is the independent variable, and a and b are constants.
In this case, the dependent variable is the maximal oxygen consumption (r), and the independent variable is the body mass (m).
So, we can write the equation as:
log(r) = a * log(m) + c, where a is the slope and c is the vertical axis intercept.
Given that the slope is approximately 0.3 (a ≈ 0.3) and the vertical axis intercept is approximately 0.101 (c ≈ 0.101), we can substitute these values into the equation:
log(r) = 0.3 * log(m) + 0.101
Using logarithmic properties, we can rewrite the equation as:
r = 10^(0.3 * log(m) + 0.101)
Simplifying further:
r = 10^(0.101) * 10^(0.3 * log(m))
Using the property: 10^(a * log(b)) = b^a
r = 10^(0.101) * (m^0.3)
Finally, we can simplify:
r = 1.107 * (m^0.3)
Therefore, the equation that relates maximal oxygen consumption (r) and body mass (m) is:
r ≈ 1.107 * (m^0.3)