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E. coli is among the fastest-growing bacteria, with a generation (or doubling) time of 20 minutes under optimal conditions. After 60 minutes, the number of bacteria in a culture of E. coli was 400 . Approximately how many bacteria were in the culture after 30 minutes?
Choose 1 answer:
(A) 50
(B) 142
(C)
174
(D) 200

E. coli is among the fastest-growing bacteria, with a generation (or doubling) time of $20$ minutes under optimal conditions. After $60$ minutes, the number of bacteria in a culture of E. coli was $400$ . Approximately how many bacteria were in the culture after $30$ minutes? $\newline$ Choose $1$ answer: $\newline$ (A) $50$ $\newline$ (B) $142$ $\newline$ (C) $174$ $\newline$ (D) $200$

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Find probabilities using the binomial distribution

Full solution

Q. E. coli is among the fastest-growing bacteria, with a generation (or doubling) time of

20

minutes under optimal conditions. After

60

minutes, the number of bacteria in a culture of E. coli was

400

. Approximately how many bacteria were in the culture after

30

minutes?

\newline

Choose

1

answer:

\newline

(A)

50

\newline

(B)

142

\newline

(C)

174

\newline

(D)

200

Understand the problem: Understand the problem. $\newline$ We know that extit{E. coli} bacteria double every $20$ minutes. After $60$ minutes, the number of bacteria is $400$ . We need to find out how many bacteria were there after $30$ minutes, which is one generation or doubling time before the count was $400$ .
Determine doublings in $60$ minutes: Determine the number of doublings that occurred in $60$ minutes. $\newline$ Since the doubling time is $20$ minutes, in $60$ minutes there would be $60 / 20 = 3$ doublings.
Calculate bacteria after one fewer doubling: Calculate the number of bacteria after one fewer doubling. $\newline$ To find the number of bacteria after $30$ minutes (which is one doubling time before $60$ minutes), we divide the number of bacteria at $60$ minutes by $2$ (because the population halves as we go back one doubling time). $\newline$ $400 / 2 = 200$

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