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Algebra / Linear functions Difficulty: Medium

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?

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Explanation

Choice A is correct. It's given that the equation $y = 0.67 x + 2.6$ , where $20 \leq x \leq 110$ , 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 $y equals 41.46$ . 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.