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 \( P(4) = 843.75 \), we need to understand what the function \( P(n) \) represents. The function calculates the insect population in generation \( n \) based on an initial population of 54 insects, with each generation being 2.5 times larger than the previous one.

In this context, \( P(4) \) corresponds to the population in the 4th generation. So:

• Since \( P(4) = 843.75 \), this means that in the 4th generation, the insect population is 843.75.

This means we can conclude that there were approximately 844 insects in the 4th generation when rounded.

Therefore, the correct interpretation is:

There were 844 insects in the 4th generation.