If the consumption rate of oxygen were to increase by a factor of 8, and given what we know about cardiac system physiology, we can confirm that the cardiac output will be four times greater than the base value.
Oxygen consumption increases in response to certain stimuli. Exercise or increased breathing due to stress are some of the many stimuli that can cause oxygen consumption to increase. In response to this, the cardiac output increases in order to move more blood, and thus more oxygen, through the body.
The relationship between these two variables is that they are directly proportional, meaning as one increases so does the other, however, the cardiac output does not increase at the same rate. This would not be necessary given that there are other factors at play that aid in increasing the blood flow, such as dilation of the arteries. Therefore, during an 8x increase in oxygen consumption, the cardiac output will increase 4x.
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