Final answer:
The statement that the non-food crop will be entirely infected after the sixth month if the infected area doubles every month is True, assuming the initial infection is a sufficiently small fraction of the total crop area.
Step-by-step explanation:
The question deals with exponential growth, a concept in mathematics where a quantity doubles at regular intervals. The pest infection on the non-food crop is described as doubling every month. Starting with any amount of infection, if it doubles every month, after the first month it will be twice the original amount, after the second month, four times, and so on until after six months, it would have doubled six times. This can be described mathematically as 2^6 (2 raised to the power of 6), which equals 64. So if we start with 1/64 of the crop infected, after six doublings, the entire crop would be infected. Therefore, the statement is True.