QuestionJuly 8, 2025

A microbiologist inoculates a growth medium with 100 bacterial cells/mL. It the generation time of this the culture contains more than 10,000 cells/ml? 3 hours. 7 hours. 2 hours. 24 hours. 10 hours.

A microbiologist inoculates a growth medium with 100 bacterial cells/mL. It the generation time of this the culture contains more than 10,000 cells/ml? 3 hours. 7 hours. 2 hours. 24 hours. 10 hours.
A microbiologist inoculates a growth medium with 100 bacterial cells/mL. It the generation time of this the culture contains more than 10,000 cells/ml? 3 hours. 7 hours. 2 hours. 24 hours. 10 hours.

Solution
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Answer

The specific time when the culture contains more than 10,000 cells/ml depends on the initial conditions and growth rate, which are not provided. Explanation 1. Identify the Growth Pattern Determine if the cell culture follows exponential growth, linear growth, or another pattern. 2. Calculate Cell Count Over Time Use the formula for exponential growth: N(t) = N_0 \cdot e^{rt}, where N_0 is the initial number of cells, r is the growth rate, and t is time in hours. 3. Solve for Time to Reach 10,000 Cells/ml Rearrange the formula to solve for t: t = \frac{\ln(N(t)/N_0)}{r}, assuming you have the values for N_0, r, and N(t) = 10,000. 4. Compare Given Times Check which of the given times (3, 7, 2, 24, 10 hours) satisfies the condition N(t) > 10,000 using the calculated growth pattern.

Explanation

1. Identify the Growth Pattern<br /> Determine if the cell culture follows exponential growth, linear growth, or another pattern.<br /><br />2. Calculate Cell Count Over Time<br /> Use the formula for exponential growth: $N(t) = N_0 \cdot e^{rt}$, where $N_0$ is the initial number of cells, $r$ is the growth rate, and $t$ is time in hours.<br /><br />3. Solve for Time to Reach 10,000 Cells/ml<br /> Rearrange the formula to solve for $t$: $t = \frac{\ln(N(t)/N_0)}{r}$, assuming you have the values for $N_0$, $r$, and $N(t) = 10,000$.<br /><br />4. Compare Given Times<br /> Check which of the given times (3, 7, 2, 24, 10 hours) satisfies the condition $N(t) > 10,000$ using the calculated growth pattern.
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