(Originais Teachy 2023) - Question Very Hard of Mathematics

A culture of bacteria grows exponentially according to the function y = 100 * (1.05)^t, where y is the number of bacteria after t hours. A laboratory needs to produce a certain amount of a substance that is produced by the bacteria. However, the substance is collected only when the number of bacteria is a power of 4. Since the laboratory has a collection window of only 24 hours, determine the ideal time to start the collection in order to obtain the largest possible amount of the substance, knowing that the start of the collection must be a multiple of 4 hours and the collection must last for a continuous period of time.