Why would we have to use the square root of 9. Was it just to simplify the answer?

answer-

the equation that models this pattern is

solution-

a researcher placed a petri dish with 32,000 bacterial cells. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved.

this can be represented as exponential decreasing function,

where,

putting the values,

y-intercept means, where x=0, so

the coordinate of this poin will be (0, 32000)

this means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

after 3 hours, number of bacteria cells will be,

the   coordinate of this point will be (3, 4000)