To interpret the meaning of \( P(4) = 843.75 \), we need to understand what \( P(n) \) represents. The function \( P(n) = 54(2.5)^{n-1} \) represents the population of the insects at generation \( n \).
When you calculate \( P(4) \), it gives the population in the 4th generation:
- \( n = 4 \)
- \( P(4) = 54(2.5)^{4-1} = 54(2.5)^3 = 54 \times 15.625 = 843.75 \)
Thus, \( P(4) = 843.75 \) indicates that in the 4th generation, there are approximately 843.75 insects. Since you typically can't have a fraction of an insect when counting populations, you could interpret this as approximately 844 insects in practical terms.
Therefore, the correct response is:
There were 844 insects in the 4th generation.