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Use the following graph to answer questions 3 and 4.
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Which of the lines best depicts the log phase of a thermophile incubated at room temperature?
7. Prokaryotic Cell Structures & Functions
Generation Times
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Calculate the number of cells that have grown after 12 hours starting from 100 cells that have a generation time of 1 hour.
A
40,960 cells
B
4,096 cells
C
4,096,000 cells
D
409,600 cells
Verified step by step guidance1
Understand that the problem involves exponential growth of a bacterial population, where the number of cells doubles every generation time.
Identify the initial number of cells, which is 100, and the generation time, which is 1 hour.
Determine the total number of generations that occur in 12 hours. Since the generation time is 1 hour, there will be 12 generations in 12 hours.
Use the formula for exponential growth: \( N = N_0 \times 2^n \), where \( N \) is the final number of cells, \( N_0 \) is the initial number of cells, and \( n \) is the number of generations.
Substitute the known values into the formula: \( N = 100 \times 2^{12} \). Calculate \( 2^{12} \) to find the final number of cells after 12 hours.
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