Final answer:
As an athlete's training progresses and blood viscosity decreases, resistance typically decreases and blood flow increases, allowing for vascular adaptations such as increased diameters of blood vessels. The radii of the blood vessels increase significantly enough to accommodate a tenfold rise in blood flow despite slight decreases in blood viscosity and rises in blood pressure during vigorous exercise such as a marathon.
Step-by-step explanation:
During vigorous exercise such as a marathon race, the body undergoes various physiological adaptations to meet the increased demand for oxygen and nutrients. One such adaptation is the change in blood viscosity and vascular homeostasis. Blood viscosity, which is the thickness of the blood, normally remains stable, but can be affected by factors like temperature, stress, and dehydration. Exercise can temporarily reduce blood viscosity, and as a result, there would be less resistance to blood flow. This decrease in resistance could contribute to the dramatic increase in blood flow required during intense physical exertion.
Athletes in training may experience adaptations that lead to an improved cardiovascular system. The heart becomes more efficient, and endurance training can even result in an increase in the diameter of blood vessels, which lowers resistance and allows for a greater volume of blood to be transported. In a well-trained athlete, blood flow can increase significantly during exercise, and blood pressure can also rise to meet the demands of their working muscles.
In the case provided, with the athlete's blood viscosity dropping to 95.0% of its normal value and the blood pressure difference increasing by 50.0%, these changes would contribute to a decrease in resistance. To determine the factor by which the average radii of her blood vessels have increased, we would use Poiseuille's Law, which describes the flow of incompressible fluids in a cylindrical pipe. The law states that flow rate is proportional to the fourth power of the radii of the vessels (radius^4), and inversely proportional to viscosity, so even a small increase in radii can greatly increase blood flow.
Considering the flow rate is 10 times the resting rate, and the viscosity decreased to 95% of normal, and that the blood pressure difference has increased by 50%, we can conclude that the radii of her blood vessels have increased significantly to accommodate this change. However, without specific numerical values for the initial radius and other factors, we cannot provide the precise factor by which the radii have increased.