Recently, frogs have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain region, Alan collects 28 frogs, marks them, and releases them. Later, he collects 110 frogs and finds that 11 of them are marked. To the nearest whole number, what is the best estimate for the frog population? ____

Question

Recently, frogs have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain region, Alan collects 28 frogs, marks them, and releases them. Later, he collects 110 frogs and finds that 11 of them are marked. To the nearest whole number, what is the best estimate for the frog population?   ____

Bytelearn · Accepted Answer

Given Information: We are given the following information: - Alan marks and releases 28 frogs. - Later, he collects 110 frogs, out of which 11 are marked. We need to estimate the total frog population in the region based on this data. We will use the capture-recapture method, which assumes that the proportion of marked frogs in the second sample represents the same proportion of the total population.Proportion Setup: Set up a proportion to represent the relationship between the marked and unmarked frogs in the second sample and the total population. Let p be the estimated frog population. The proportion is as follows: (marked frogs in second sample) / (total frogs in second sample) = (total marked frogs) / (estimated total population) 11 / 110 = 28 / pCross Multiplication: Cross multiply to solve for p: 11 * p = 28 * 110Solving for p: Now, divide both sides of the equation by 11 to solve for p: (11 * p) / 11 = (28 * 110) / 11 p = (28 * 110) / 11Calculating p: Calculate the value of p: p = (28 * 110) / 11 p = 3080 / 11 p = 280

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