Question

for a research study, 64 marmots were tagged and set free. later, the researchers returned to the site and found 36 tagged marmots out of the 900 marmots they counted. to the nearest whole number, what is the best estimate for the marmot population?

Explanation:

Step1: Set up proportion

Let \( x \) be the total population. The proportion of tagged marmots in the sample should equal the proportion of tagged marmots in the population. So, \(\frac{64}{x}=\frac{36}{900}\)

Step2: Cross - multiply and solve for \( x \)

Cross - multiplying gives \( 36x = 64\times900 \). First, calculate \( 64\times900 = 57600 \). Then, solve for \( x \) by dividing both sides by 36: \( x=\frac{57600}{36} \)

Step3: Calculate the value of \( x \)

\(\frac{57600}{36}=1600\)

Answer:

1600