Question

joe is a scientist who works with the department of agriculture. in order to ensure a good harvest, joe keeps track of various local beetle populations. he catches 590 beetles, marks them, and releases them. then later, he catches 2,000 beetles, 59 of which are marked. to the nearest whole number, what is the best estimate for the beetle population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total beetle population. The proportion of marked beetles in the first catch to the total population should equal the proportion of marked beetles in the second catch to the number of beetles in the second catch. So we have \(\frac{590}{N}=\frac{59}{2000}\).

Step2: Solve for \( N \)

Cross - multiply to get \( 59N = 590\times2000 \). Then \( N=\frac{590\times2000}{59} \). First, simplify \( \frac{590}{59}=10 \), so \( N = 10\times2000=20000 \).

Answer:

20000