The number of bacteria in a certain dish over a 5-hour period is modeled by the function f defined above, where t represents time, in hours. According to the model, how many bacteria were in the dish at time t = 0?

Rationale

There were 100 bacteria in the dish at time t = 0.

At time t = 0, the function f(t) evaluates to the initial number of bacteria present, which is given as 100. This value represents the starting point of the bacteria's growth model over the specified time period.

A (0) YOUR ANSWER

If there were 0 bacteria at time t = 0, it would imply that the bacteria were not present in the dish at the beginning of the observation. However, the function explicitly starts with an initial count of 100, making this choice incorrect.

B (50) YOUR ANSWER

Choosing 50 as the initial count would suggest that half of the actual starting amount of bacteria was present at time t = 0. This contradicts the information given, as the model specifies the starting quantity to be 100, not 50, making this option incorrect.

C (100) CORRECT

The function indicates that at t = 0, the number of bacteria is 100. This is the correct answer, as it reflects the initial condition of the model before any growth has occurred.

D (200) YOUR ANSWER

Selecting 200 as the initial count would imply that the bacteria population started at a higher number than indicated by the model. Since the function specifies the starting point as 100, this option is also incorrect.

Conclusion

The initial number of bacteria in the dish at time t = 0 is clearly defined as 100 in the model provided. Each incorrect option misrepresents this initial condition, emphasizing the importance of accurately interpreting mathematical functions and their parameters. Thus, understanding the starting value is crucial for analyzing the growth of the bacteria over time.

The number of bacteria in a certain dish over a 5-hour period is modeled by the function f defined above, where t represents time, in hours. According to the model, how many bacteria were in the dish at time t = 0?

There were 100 bacteria in the dish at time t = 0.

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