Final answer:
The described immunity is naturally acquired active immunity, where the body adapts to a pathogen through infection and forms long-lasting immunological memory.
Step-by-step explanation:
The type of adaptive immunity described by the student, where immunity is acquired after antigens enter the body naturally through infection and the immune system creates an immunological memory of that particular antigen, is called naturally acquired active immunity.
This form of immunity is a result of the body's own adaptive immune response to a pathogen. During this response, memory B cells and memory T cells are formed, which provide long-term protection against the specific pathogen, affording rapid and powerful response upon reexposure. In naturally acquired active immunity, the adaptive immune system is activated by exposure to infectious agents, and this can lead to long-lasting immunity.