Question

for a science fair project, a group of students decides to estimate the population of muskrats living in the nearby forest. they trap 148 muskrats and mark them. then, a week later, they return to the forest and trap 490 muskrats, 37 of which are marked. to the nearest whole number, what is the best estimate for the muskrat population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked muskrats in the first sample should equal the proportion of marked muskrats in the second sample. So we have \(\frac{148}{N}=\frac{37}{490}\).

Step2: Solve for \( N \)

Cross - multiply: \( 37N = 148\times490 \). Then \( N=\frac{148\times490}{37} \). First, calculate \( 148\div37 = 4 \). Then \( N = 4\times490=1960 \).

Answer:

1960