Final answer:
Mutant cells require tyrosine for growth because they are auxotrophs with a specific mutation impairing the biosynthesis of tyrosine, thus dependence on external supply of the amino acid.
Step-by-step explanation:
The mutant cells discussed require tyrosine to grow when it is added to the bacteriophage because they are likely auxotrophs. Auxotrophs are bacterial mutants that have lost the ability to synthesize a specific nutrient due to a mutation in a gene encoding an enzyme in the biosynthesis pathway.
In the case of tyrosine, the mutation may impair the enzyme responsible for its synthesis, and therefore, the cells can only grow when tyrosine is exogenously supplied. The importance of adding cells to both nutrient-deficient plates and a nutritionally complete plate during replica plating is to ensure proper transfer of cells and to identify which mutants specifically require the missing nutrient for growth, in this case tyrosine.