Question

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 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 844 insects in the 4th generation. There were 844 insects in the 4th generation. There were 4 insects in the 843rd generation. There were 4 insects in the 843rd generation. There were 4 insects in the 844th generation. There were 4 insects in the 844th generation.

Answer 1

To interpret the meaning of $P(4)=843.75$ in the context of the insect population, we look at the function $P(n)=54(2.5{)}^{n-1}$.

Calculating $P(4)$:

$$P(4)=54(2.5{)}^{4-1}=54(2.5{)}^3$$ $$(2.5{)}^3=15.625$$ $$P(4)=54\times 15.625=843.75$$

This value of 843.75 represents the population of the insect species in the 4th generation. However, since insect populations are typically counted in whole numbers (you can't have a fraction of an insect), the correct interpretation would be that in the 4th generation, the population is approximately 844 insects (rounding 843.75 up).

Given the options you've provided, the correct response is:

There were 844 insects in the 4th generation.