Question

An ecologist wants to estimate the total number of blackbirds that live in an area. He captures some blackbirds, marks them with a dye and then releases them. A few days later, he captures 40 blackbirds and finds that 16 are marked. He estimates the total number of blackbirds to be 200. Work out how many blackbirds the ecologist marked.​

Answer 1

By using the mark and recapture method and setting up a proportion (M/200 = 16/40), it can be calculated that the ecologist initially marked 80 blackbirds.

Step-by-step explanation:

The ecologist used a method known as mark and recapture to estimate the total number of blackbirds in an area. If the ecologist estimated the total population size (N) to be 200, and upon recapture, found out that 16 of the 40 blackbirds were marked, we can set up a proportion to solve for the number of marked blackbirds originally (M).

The proportion is based on the assumption that the ratio of marked blackbirds in the second sample (16 out of 40) should be the same as the ratio of the total marked blackbirds to the entire population (M to 200).

Thus, the equation is:

M / 200 = 16 / 40

After cross-multiplying we get:

M x 40 = 16 x 200

M = (16 x 200) / 40

M = 3200 / 40

M = 80

Therefore, the ecologist must have marked 80 blackbirds initially.