to determine the number of trout in a lake a conservationist catches 144 trout, tags them and throws them back into the lake. later 28 trout are caught; 14 of them are tagged. how many trout would the conservationist expect to be in the lake?
apparently 14/28 = 50% of the trout have tags.
To determine the estimated number of trout in the lake, we can use a method called the capture-recapture method or the Lincoln-Petersen index. This method is commonly used in ecology to estimate the population size of animals.
The basic idea behind the capture-recapture method is that the ratio of tagged to untagged individuals in a second sample is proportional to the ratio of tagged to untagged individuals in the entire population.
In this case, let's break down the information provided:
1. Initially, the conservationist catches and tags 144 trout.
2. Later, a new sample of 28 trout is caught, out of which 14 are tagged.
Now, we can set up a proportion using the information from the first sample and the second sample:
(Tagged trout in first sample / Total number of trout in the lake) = (Tagged trout in second sample / Total number of trout in the lake)
Let's substitute the values we have:
(144 / X) = (14 / 28)
We can cross-multiply and solve for X, which represents the total number of trout in the lake:
14X = 144 * 28
X = (144 * 28) / 14
X = 288
Therefore, the conservationist would expect there to be approximately 288 trout in the lake based on the given information and using the capture-recapture method.