Biologists use algebra to estimate the number of fish in a lake. they first catch a sample of fish and mark each specimen with a harmless tag. some weeks later, they catch a similar sample of fish from the same areas of the lake and determine the proportion of previously tagged fish in the new sample. the total fish population is estimated by assuming that the proportion of tagged fish in the new sample is the same as the proportion of tagged fish in the entire lake. suppose biologists tagged 300 fish on may 1. when they returned on june 1, and took a new sample of 400 fish, 5 of the 400 were previously tagged. estimate the number of fish in the lake.
Solution: Sure, here is the solution:
The proportion of tagged fish in the new sample is 5/400 = 1/80.
We can estimate the total fish population by assuming that the proportion of tagged fish in the new sample is the same as the proportion of tagged fish in the entire lake.
This means that 1/80 of the fish in the lake are tagged.
If 300 fish are tagged, then the total number of fish in the lake is 300 * 80 = 24,000.
So the answer is 24,000