Question

an organic farm controls pests with the number of praying mantis larvae released on the farm by the equation
$p(n) = 1000 - 2.5n$
where $n$ is the number of larvae released per acre and $p$ is the number of pests per acre. which of these statements most accurately describes this function?
\bigcirc as $n$ gets to some value, $p$ should go to zero.
\bigcirc the pests can only be minimized, never exterminated.
\bigcirc organic farming can never be cost effective.
\bigcirc more praying mantis larvae lead to more pests.

Explanation:

1. Analyze the linear function $p(n) = 1000 - 2.5n$: as $n$ (number of larvae) increases, $p$ (number of pests) decreases.
2. Set $p(n)=0$ and solve:

$$0 = 1000 - 2.5n$$
$$2.5n = 1000$$
$$n = 400$$
When 400 larvae per acre are released, the pest count reaches zero, matching the first statement. The other options are incorrect: the function shows pests can reach zero (so they can be exterminated), cost effectiveness is not addressed, and more larvae reduce pests, not increase them.

Answer:

As n gets to some value, p should go to zero.