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?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked caterpillars in the first catch to the total population should equal the proportion of marked caterpillars in the second catch to the number of caterpillars in the second catch. So we have \(\frac{750}{N}=\frac{12}{400}\).

Step2: Solve for \( N \)

Cross - multiply: \( 12N = 750\times400 \). Then \( N=\frac{750\times400}{12} \). First, calculate \( 750\times400 = 300000 \). Then divide by 12: \( N=\frac{300000}{12}=25000 \).

Answer:

25000