Scientists often use the catch, band, and release method to estimate the size of wildlife populations. For example, 250 trout were caught, banded, and released into a small lake in Northern Ontario. One month later, another 250 trout were caught in the lake, 30 of them had bands. From this information scientists could estimate the size of the trout population of the lake. What is the expected population of trout? How do you know?

Question

Mathematics

Davion Schmidt

1 April, 00:20

Scientists often use the catch, band, and release method to estimate the size of wildlife populations. For example, 250 trout were caught, banded, and released into a small lake in Northern Ontario. One month later, another 250 trout were caught in the lake, 30 of them had bands. From this information scientists could estimate the size of the trout population of the lake. What is the expected population of trout? How do you know?

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Answers (1)

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Shawn Beck · Answer 1

2083.33 trouts

Step-by-step explanation:

Total population of fish in the pond is unknown, therefore, let's us represent this using letter Z

The ratio of banded, caught and released trout to the total trout population is represented as 250 : Z

We can solve this type of problem with a proportion:

Total number of fishes that was tagged and caught / Total number of fishes that was caught = Total number of tagged fishes in the pond / Total number of fishes in the pond.

In the question, we were given this values:

Total number of banded trout's that was caught and released into the pond = 250

Total number of trouts that was caught and had bands in the lake = 30

Total number of trouts that was caught in the lake = 250

Total number of fishes in the pond = Z

Hence we have:

30/250 = 250 / Z

We cross mulitply

30 * Z = 250 * 250

30Z = 62500

We divide both sides by 30

30Z / 30 = 62500/30

Z = 2083.33

Therefore, the expected population of trout is 2083.33 trouts