Question

recently, bats have been disappearing from the wild due to a contagious fungus. to monitor the current population in a certain region, troy collects 78 bats, marks them, and releases them. later, troy collects 600 bats, and finds that 39 of them are marked. to the nearest whole number, what is the best estimate for the bat population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total bat population. The proportion of marked bats in the first sample (marked) to the total population should equal the proportion of marked bats in the second sample (recaptured) to the number of bats in the second sample. So we have \(\frac{78}{N}=\frac{39}{600}\).

Step2: Solve for \( N \)

Cross - multiply: \( 39N = 78\times600 \). Then \( N=\frac{78\times600}{39} \). First, calculate \( 78\div39 = 2 \), so \( N = 2\times600=1200 \).

Answer:

1200