(Originais Teachy 2023) - Question Medium of Mathematics

In an experiment, the number of microorganisms in a culture grows according to a rate that can be modeled by a logarithmic function. After a detailed analysis, a group of students obtained the graph of the logarithmic function that describes the growth of this culture, which passes exactly through the point (1,2). Considering that the base of the logarithm used is 'e', identify the mathematical expression that represents the logarithmic function of the growth of microorganisms, and justify your answer by explaining how the information of the point (1,2) on the graph is crucial to determine the function. Additionally, determine the number of microorganisms in the culture after 4 units of time, using the concept of logarithmic function and the values from the graph, without the need for exact logarithm calculations.