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During a biology class, the 1st year of high school at a college divided the class into groups to carry out an experiment that analyzed the biotic potential of some populations of bacteria and a total of 2 hours for observation and notes.
GROUP A:
The initial population corresponded to (2 · n + 18) bacteria;
After 1 hour, the population doubled;
2 hours later
population there
quadrupled compared to the initial.
GROUP B:
The initial population corresponded to (81 · n - 69) bacteria;
After the start, in 1 hour the resulting number of bacteria was equal to the initial one, plus double that number;
After 2 hours they realized that the number of bacteria was the initial number, plus the quadruple of that number.
GROUP C:
The initial population corresponds to (46 · n) bacteria;
30 minutes later, the population tripled;
After 1 hour, the population was six times more than the initial population.
After 5 hours, the teacher went to check the notes made and realized that all of them were true and that the behavior previously presented was maintained in each group throughout this time. In order to organize these values, the teacher used a matrix, and created the matrix A = (aij) 3x3, where "i" represented time in an increasing way, and "j" the groups, in alphabetical order. the values chosen for organization were the initial, 2 hours later and 5 hours after the beginning of the experiment. in order to further facilitate the organization of the data obtained, the teacher calculated the determinant of this matrix. What is the value of this determinant obtained by the teacher?
