In the general exponential equation \( a_n = a_1 \cdot r^{n-1} \), \( a_1 \) represents the initial value of the population at \( n = 1 \).
Given in the problem, the initial population of the bacteria is 50. Thus, \( a_1 \) is simply the initial population.
Therefore, the value of \( a_1 \) is 50.