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Multiple Choice
A microbiologist is having a population of 300 E. coli bacteria in an experiment in her lab. E. coli's generation time is 15 minutes. The scientist lets the E. coli population grow for 1 hour and 45 minutes. How many E. coli bacteria are present after this time?
A
29,700 cells
B
38,400 cells
C
600,000 cells
D
308,400 cells
Verified step by step guidance
1
Determine the total time the E. coli population is allowed to grow. Convert 1 hour and 45 minutes into minutes: 1 hour = 60 minutes, so 1 hour and 45 minutes = 60 + 45 = 105 minutes.
Calculate the number of generations that occur in 105 minutes. Since the generation time is 15 minutes, divide the total time by the generation time: 105 minutes / 15 minutes per generation = 7 generations.
Use the formula for exponential growth to calculate the final population size: N = N0 * 2^n, where N0 is the initial population size, n is the number of generations, and N is the final population size.
Substitute the known values into the formula: N0 = 300 (initial population), n = 7 (number of generations). Therefore, N = 300 * 2^7.
Calculate 2^7 to find the growth factor, then multiply by the initial population (300) to find the final population size after 7 generations.