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 0.5 and the vertical axis intercept of approximately 0.105. Find an equation that relates maximal oxygen consumption, r, and body mass, m.
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Did you hear about the wild African mammal who loved oxygen? He was always chasing it around the savannah and trying to catch it! Now, let's find an equation to relate their maximal oxygen consumption, r, and body mass, m.
In this case, we have a log-log plot, which means we take the logarithm of both the x-axis (body mass) and y-axis (maximal oxygen consumption) values. The slope of the straight line is approximately 0.5, and the vertical axis intercept is approximately 0.105.
So, let's write the equation in log form: log(r) = 0.5 * log(m) + 0.105
Now, let's bring the exponent back outside the logarithm: r = 10^(0.5 * log(m) + 0.105)
But wait! We can further simplify this equation. Remember that raising 10 to the power of the sum of logarithms is the same as multiplying the numbers under the logarithms. Also, raising 10 to the power of log(m) eliminates the logarithm, leaving us with just m.
After simplifying, the equation becomes: r = 10^(0.5) * m^(0.105)
So, the equation that relates maximal oxygen consumption, r, and body mass, m is: r = 3.16228 * m^(0.105)
Keep in mind that this equation is only an approximation based on the given data and slope, so use it with caution!
To find an equation that relates maximal oxygen consumption, r, and body mass, m, we can use the equation of a straight line.
In a log-log plot, the equation of a straight line can be written as:
log(r) = log(a) + b * log(m)
where r is the maximal oxygen consumption rate, m is the body mass, a is the vertical axis intercept, and b is the slope of the line.
Since the vertical axis intercept is approximately 0.105 and the slope is approximately 0.5, the equation becomes:
log(r) = log(0.105) + 0.5 * log(m)
To simplify further, we can use the logarithmic identity log(ab) = b * log(a). Applying this identity:
log(r) = log(0.105) + log(m^0.5)
log(r) = log(0.105) + 0.5 * log(m^2)
Again, using the logarithmic identity log(a^b) = b * log(a):
log(r) = log(0.105) + log(m)
log(r) = log(0.105m)
Now, exponentiating both sides of the equation:
r = 0.105m
Therefore, the equation that relates maximal oxygen consumption, r, and body mass, m, is r = 0.105m.
To find an equation that relates maximal oxygen consumption (r) and body mass (m) based on the given information, we need to use the slope and vertical axis intercept.
The equation for a straight line on a log-log plot is given by:
y = mx + b
In this case, the maximal rates of oxygen consumption (r) correspond to the y-values, and the body mass (m) corresponds to the x-values.
We know that the slope (m) is approximately equal to 0.5 and the vertical axis intercept (b) is approximately equal to 0.105.
Therefore, the equation relating maximal oxygen consumption (r) and body mass (m) is:
r = 0.5 * m + 0.105