Terrence is a scientist who works with the Department of Agriculture. In order to ensure a good harvest, Terrence keeps track of various local caterpillar populations. He catches 750 caterpillars, marks them, and releases them. Then later, he catches 400 caterpillars, 12 of which are marked. To the nearest whole number, what is the best estimate for the caterpillar population? ____

Question

Terrence is a scientist who works with the Department of Agriculture. In order to ensure a good harvest, Terrence keeps track of various local caterpillar populations. He catches 750 caterpillars, marks them, and releases them. Then later, he catches 400 caterpillars, 12 of which are marked. To the nearest whole number, what is the best estimate for the caterpillar population?   ____

Bytelearn · Accepted Answer

Set up proportion: Set up the proportion based on the mark and recapture data. Marked caterpillars found: 12 Total caterpillars in second catch: 400 Total caterpillars marked initially: 750 Let $ p $ be the estimated caterpillar population. The proportion is: $$ \frac{\text{marked caterpillars found}}{\text{total caterpillars in second catch}} = \frac{\text{total caterpillars marked initially}}{\text{estimated caterpillar population}} $$ $$ \frac{12}{400} = \frac{750}{p} $$Solve for p: Solve for $ p $ by cross-multiplying. $$ 12 \cdot p = 750 \cdot 400 $$ $$ 12p = 300000 $$Divide to isolate p: Divide both sides by 12 to isolate $ p $. $$ p = \frac{300000}{12} $$ $$ p = 25000 $$

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