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podryga
1 month ago
12

The E. coli bacteria has a volume of 6 µm3 . In optimal conditions, an E. coli bacteria will double about every 30 minutes. Unde

r these conditions, how long will it take for a single bacterium to grow to fill a thimble with volume 1 cm3 ? How long will it take for the volume to fill the entire earth 1.08 × 108 km3 ?
Mathematics
1 answer:
babunello [11.8K]1 month ago
4 0
Answer: It would take approximately 19 hours and 15 minutes for one bacterium to grow and occupy the volume of a thimble measuring 1 cm3. In contrast, filling the entire Earth would require 57.6 hours. Step-by-step explanation: The growth of the bacteria can be modeled as a geometric sequence, with the time intervals forming an arithmetic sequence. Each geometric sequence is structured as follows: where 'a' represents the initial term and 'r' denotes the common ratio. Any term of the sequence can be calculated using the subsequent formula: Each arithmetic sequence has its format, defined as follows: in which 'a' is the first term and 'd' indicates the difference between the terms. The corresponding formula to locate any term in the sequence is provided. To solve this issue, we analyze the volume related to the bacterium growth. Note: Following this, we address the arithmetic sequence detailing the time in hours. The question is about determining how long it takes for a single bacterium to suffice for a thimble of volume 1 cm3. We will ascertain the value of 'n,' afterwards identifying its position in the arithmetic sequence. Note: We will apply certain logarithmic properties to find 'n': log 2 = 0.30 and log 3 = 0.48. Now, let's find the respective values in the arithmetic series. It takes roughly 19 hours and 15 minutes for a single bacterium to fill a thimble 1 cm3 in size. As for the time taken to fill the entire Earth, measured at 1.08 × 108 km3, we proceed in the same manner as before.
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