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 second count should be equal to the proportion of tagged bobcats in the total population. So we have \(\frac{54}{972}=\frac{79}{x}\).

Step2: Cross - multiply

Cross - multiplying gives us \( 54x = 79\times972 \).

Step3: Solve for \( x \)

First, calculate \( 79\times972 = 77788 \). Then, \( x=\frac{77788}{54}\approx1440.5185\). Rounding to the nearest whole number, we get \( x\approx1441 \).

Answer:

1441