An 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

Question

represents the insect population for generation n. Interpret the meaning of P(4)=843.75
.(1 point)
Responses

There were 843 insects in the 4th generation.
There were 843 insects in the 4th generation.

There were 4 insects in the 844th generation.
There were 4 insects in the 844th 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.

Answer 1

To interpret \( P(4) = 843.75 \) in the context of the insect population model given by \( P(n) = 54(2.5)^{n-1} \):

• The function \( P(n) \) calculates the population of insects in generation \( n \).
• When \( n = 4 \), the output \( P(4) = 843.75 \) indicates the insect population in the 4th generation.

Since \( P(4) = 843.75 \), the correct interpretation is that there were 843.75 insects in the 4th generation.

However, since we typically cannot have a fractional insect in practical terms, it's reasonable to round this number. Thus, we would say there were approximately 844 insects in the 4th generation.

Therefore, the most appropriate response from the options provided is: There were 844 insects in the 4th generation.