人教版高中生物学教材中有“细胞大小与物质运输关系”的模拟实验,以琼脂块和NaOH溶液分别模拟细胞和细胞所需要的物质。通过建构数学模型来领悟细胞大小与物质运输的关系。设正方体的琼脂块边长为x,NaOH扩散深度为a,且x≥2a,a>0(扩散深度不能超过边长的一半)(图1)。该实验中NaOH在琼脂块中的扩散速率相同(单 PEP teaches a simulation experiment of the relationship between cell size and matter transport in high school biology textbooks. The agar block and NaOH solution simulate the substances required for cells and cells, respectively. Construct a mathematical model to understand the relationship between cell size and material transport. Set the agar cube side length x, NaOH diffusion depth a, and x ≥ 2a, a> 0 (diffusion depth can not exceed half of the side length) (Figure 1). The NaOH diffusion rate in the agar block is the same in this experiment (single