(Originais Teachy 2023) - Question Hard of Mathematics

A scientist is studying the population growth of a species of bacteria in a laboratory, and he observes that the number of bacteria doubles every 3 hours. Initially, the laboratory had 100 bacteria. To monitor the population growth, the scientist uses the logarithmic function to represent the number of bacteria as a function of time. Considering the base of the logarithm as 2, which is the base of exponential growth when a quantity doubles, and knowing that the logarithmic function is the inverse of the exponential function, determine: 1) The logarithmic function that represents the number of bacteria in the laboratory as a function of time, using the initial time as t = 0. 2) The number of bacteria in the laboratory after 9 hours, using the found logarithmic function. Present detailed calculations to justify your answer.