Final answer:
The question revolves around the biological and agricultural concepts of nitrogen fixation and its significance in crop yield. An empirical model outlines this relationship, while the production of synthetic nitrogen fertilizers has greatly impacted the carrying capacity of arable land.
Step-by-step explanation:
The student's question is related to the yield of an agricultural crop as a function of the nitrogen level in the soil, and it closely ties into the biological process of nitrogen fixation. Nitrogen fixation is essential for improving crop yield as it allows plants to absorb nitrogen in a bioavailable form to compete with weeds. An empirical model is used to depict this relationship mathematically, which is based on observations such as the increased growth rate of crops with higher soil temperatures. However, it's important to note the limitations of this model since it may simplify the complex interactions between growth and temperature. Additionally, the production and use of synthetic nitrogen fertilizers have considerably increased the supportable human population on arable land by making nitrogen available to plants, despite the inert nature of atmospheric nitrogen.