Question

to determine the bobcat population, scientists tagged 79 bobcats. later, they counted 972 bobcats, of which 54 had tags. to the nearest whole number, what is the best estimate for the bobcat population?

Explanation:

Step1: Set up proportion

Let \( x \) be the bobcat population. The proportion of tagged bobcats in the population should be equal to the proportion of tagged bobcats in the counted sample. So we have \(\frac{79}{x}=\frac{54}{972}\).

Step2: Solve for \( x \)

Cross - multiply: \( 54x = 79\times972 \). First, calculate \( 79\times972 = 79\times(900 + 72)=79\times900+79\times72 = 71100+5688 = 76788 \). Then, \( x=\frac{76788}{54}\).

Step3: Calculate the value

\( \frac{76788}{54}=1422 \).

Answer:

1422