Final answer:
The correct type of epithelia that regulates the exchange of nongaseous material is the simple cuboidal epithelium due to its specialization in secretion and absorption of ions and nutrients.
Step-by-step explanation:
The type of epithelia described in the question which actively and selectively regulates the exchange of nongaseous material, including ions and nutrients, and responds to various stimuli is known as simple cuboidal epithelium. This is due to its functions in secretory activity and absorption, often found in glandular tissues and in the ducts of organs such as the kidney and liver. Simple squamous epithelia, by contrast, typically facilitate only the exchange of gases through diffusion.
Referring to the options provided in the question, simple squamous epithelium is associated with gas exchange due to its thin, flat cells that facilitate diffusion, as mentioned in Figure 24.7a. In contrast, stratified squamous epithelium provides protection against abrasion and is not primarily involved in selective transport of non-gaseous materials. Simple cuboidal epithelium consists of cube-shaped cells specialized in secretion and absorption, functioning in the active transport of nutrients, making it the correct answer to the student's question (option 'c').
Simple columnar epithelium, although mentioned in the student's list of options, is characterized by tall, narrow cells and is typically associated with absorption and secretory functions, particularly in the digestive tract but is not the primary epithelial type for selective and regulated material exchange.