To explain why the amount of oxygen taken up into the blood increases after exercise, we need to look at both the volume of air per breath and the number of breaths per minute at rest and after running. Here's a detailed step-by-step solution:
1. Understanding the parameters at rest and after running:
- At rest:
- The volume of air per breath is [tex]\(450 \, \text{cm}^3\)[/tex].
- The number of breaths per minute is 20.
- After running:
- The volume of air per breath is [tex]\(1000 \, \text{cm}^3\)[/tex].
- The number of breaths per minute is 38.
2. Calculate the total volume of air per minute at rest:
- The total volume of air per minute at rest is given by the product of the volume of air per breath and the number of breaths per minute.
- [tex]\[
\text{Total volume at rest} = 450 \, \text{cm}^3 \times 20 = 9000 \, \text{cm}^3
\][/tex]
3. Calculate the total volume of air per minute after running:
- The total volume of air per minute after running is also given by the product of the volume of air per breath and the number of breaths per minute.
- [tex]\[
\text{Total volume after running} = 1000 \, \text{cm}^3 \times 38 = 38000 \, \text{cm}^3
\][/tex]
4. Find the difference in the total volume of air per minute between rest and after running:
- To understand the increase in oxygen uptake, we subtract the total volume of air per minute at rest from the total volume of air per minute after running.
- [tex]\[
\text{Difference in volume} = 38000 \, \text{cm}^3 - 9000 \, \text{cm}^3 = 29000 \, \text{cm}^3
\][/tex]
5. Explanation:
- After exercise, both the volume of air per breath and the number of breaths per minute increase significantly. This results in a higher total volume of air being inhaled per minute compared to when the person is at rest.
- The increased total volume of air allows for more oxygen to be taken into the lungs and subsequently into the blood. Therefore, the amount of oxygen taken up into the blood increases after exercise.
In summary, the amount of oxygen taken into the blood after exercise increases because the total volume of air per minute increases from [tex]\(9000 \, \text{cm}^3\)[/tex] at rest to [tex]\(38000 \, \text{cm}^3\)[/tex] after running, resulting in a difference of [tex]\(29000 \, \text{cm}^3\)[/tex] of air per minute. This increased airflow allows for more oxygen to be available for uptake into the bloodstream.
