Question

3 multiple choice 4 points 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? more praying mantis larvae lead to more pests. the pests can only be minimized, never exterminated. organic farming can never be cost effective. as n gets to some value, p should go to zero.

Explanation:

Step1: Analyze the function

The function is $p(n)=1000 - 2.5n$. The coefficient of $n$ is - 2.5, which means as $n$ (number of larvae released per acre) increases, $p$ (number of pests per acre) decreases.

Step2: Check each option

• Option 1: Since the coefficient of $n$ is negative, more praying - mantis larvae lead to fewer pests, not more. So this option is incorrect.
• Option 2: Set $p(n)=0$, we get $0 = 1000-2.5n$. Solving for $n$ gives $n=\frac{1000}{2.5}=400$. So pests can be exterminated when $n = 400$, and this option is incorrect.
• Option 3: The given function is about the relationship between number of larvae and number of pests, not about cost - effectiveness of organic farming. So this option is incorrect.
• Option 4: Set $p(n)=0$, we have $0=1000 - 2.5n$. Solving for $n$:

$$
LATEXBLOCK0
$$

When $n = 400$, $p$ goes to zero. This option is correct.

Answer:

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