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

𝑃
(
𝑛
)
=
54
(
2.5
)
𝑛
−
1
represents the insect population for generation n. Interpret the meaning of P(4)=843.75
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 4 insects in the 843rd generation.
There were 4 insects in the 843rd 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.

Answer 1

To interpret \( P(4) = 843.75 \) accurately:

The function \( P(n) = 54(2.5)^{n-1} \) calculates the population of insects in the \( n \)-th generation, starting from 54 insects in the first generation.

When we evaluate \( P(4) \):

• The input \( n = 4 \) indicates we are looking for the population in the 4th generation.
• The output \( P(4) = 843.75 \) means that there are approximately 843.75 insects in the 4th generation.

Since insect populations are typically considered as whole numbers, we interpret this as an indication of growth, even if the specific number isn't a whole insect.

Thus, the correct interpretation is:

There were 843 insects in the 4th generation.