Question
n insect population is growing such that each new generation is 2.5 times as large as the previous generation. Suppose there were 54 insects in the first generation. The function P(n)=54(2.5)n−1
represents the insect population for generation n. Interpret the meaning of P(4)=843.75
.(1 point)
Responses
There were 4 insects in the 844th generation.
There were 4 insects in the 844th generation.
There were 843 insects in the 4th generation.
There were 843 insects in the 4th generation.
There were 844 insects in the 4th generation.
There were 844 insects in the 4th generation.
There were 4 insects in the 843rd generation.
represents the insect population for generation n. Interpret the meaning of P(4)=843.75
.(1 point)
Responses
There were 4 insects in the 844th generation.
There were 4 insects in the 844th generation.
There were 843 insects in the 4th generation.
There were 843 insects in the 4th generation.
There were 844 insects in the 4th generation.
There were 844 insects in the 4th generation.
There were 4 insects in the 843rd generation.
Answers
GPT-4o mini
To interpret the meaning of \( P(4) = 843.75 \) in the context of the given function \( P(n) = 54(2.5)^{n-1} \):
- The notation \( P(n) \) represents the insect population in the nth generation.
- Given \( P(4) = 843.75 \), it means that in the 4th generation, the population of insects is 843.75.
Since populations are generally counted as whole numbers, we can imply that it represents an approximate or expected value for the number of insects in the 4th generation, but we generally don't have fractions of insects.
Thus, the correct interpretation is:
**There were approximately 844 insects in the 4th generation.**
However, this option is not explicitly listed. Instead, the accurate representation of the calculation would be:
**There were 843 insects in the 4th generation (rounded down).**
None of the provided options are phrased accurately according to common interpretations of population counts or rounding practices. If you have to choose from the given options, it would be best to clarify this rounding issue.
- The notation \( P(n) \) represents the insect population in the nth generation.
- Given \( P(4) = 843.75 \), it means that in the 4th generation, the population of insects is 843.75.
Since populations are generally counted as whole numbers, we can imply that it represents an approximate or expected value for the number of insects in the 4th generation, but we generally don't have fractions of insects.
Thus, the correct interpretation is:
**There were approximately 844 insects in the 4th generation.**
However, this option is not explicitly listed. Instead, the accurate representation of the calculation would be:
**There were 843 insects in the 4th generation (rounded down).**
None of the provided options are phrased accurately according to common interpretations of population counts or rounding practices. If you have to choose from the given options, it would be best to clarify this rounding issue.