Question

to estimate the number of moths in a certain region, savannah traps 168 moths and marks them. she releases these moths and then later catches 498, 28 of which are marked. to the nearest whole number, what is the best estimate for the moth population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked moths in the first sample should equal the proportion of marked moths in the second sample. So, \( \frac{\text{marked initially}}{\text{total population}}=\frac{\text{marked in second catch}}{\text{second catch size}} \), which gives \( \frac{168}{N}=\frac{28}{498} \).

Step2: Solve for \( N \)

Cross - multiply: \( 28N = 168\times498 \). First, calculate \( 168\times498 = 168\times(500 - 2)=168\times500-168\times2 = 84000 - 336 = 83664 \). Then, \( N=\frac{83664}{28} \).

Step3: Calculate the value

\( \frac{83664}{28}=2988 \).

Answer:

2988