Estimating PopulationsBiologists sometimes use direct variation to estimate the number of fish in small lakes. They start by tagging a small number of fish and then releasing them. They assume that over a period of time, the tagged fish distribute themselves evenly throughout the lake. Later, they collect a second sample. The total number of fish and the number of tagged fish in the second sample are counted. To determine the total population of fish in the lake, biologists assume that the proportion of tagged fish in the second sample is equal to the proportion of tagged fish in the entire lake. This technique can also be used to count other types of animals, such as birds, when they are not migrating.
Sixty-three blackbirds are tagged and released. Later it is estimated that out of a sample of 32 blackbirds, only 8 are tagged. Estimate the population of blackbirds in the area.
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