Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure.

Question

Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has $x$ worker ants, the equation $y = 0.67 x + 2.6$ , where $20 \leq x \leq 110$ , gives the predicted number of larvae, $y$ , in the colony. If one of these colonies has $58$ worker ants, which of the following is closest to the predicted number of larvae in the colony?

A.

$41$

B.

$61$

C.

$83$

D.

$190$

Accepted Answer

Choice A is correct. It's given that the equation y = 0.67 x + 2.6 , where 20 &#8804; x &#8804; 110 , gives the predicted number of larvae, y , in a colony of ants if the colony has x worker ants. If one of these colonies has 58 worker ants, the predicted number of larvae in that colony can be found by substituting 58 for x in the given equation. Substituting 58 for x in the given equation yields y = 0.67 58 + 2.6 , or y = 41.46 . Of the given choices, 41 is closest to the predicted number of larvae in the colony. Choice B is incorrect. This is closest to the predicted number of larvae in a colony with 87 worker ants. Choice C is incorrect. This is closest to the number of worker ants for which the predicted number of larvae in a colony is 58 . Choice D is incorrect. This is closest to the predicted number of larvae in a colony with 280 worker ants.

Question 0f9a48