A group of researchers wanted to monitor the trout population, so they marked 340 trout with tags. Later, they captured 600 trout and found that 30 of them had tags. What is the BEST estimate for the trout population?
A 6,200
B 6,600
C 6,400
D 6,800
Using a proportion, we can estimate the population:
340 tagged trout / x total population = 30 tagged trout / 600 captured trout
Solving for x, we get:
x = (340 * 600) / 30 = 6800
Therefore, the best estimate for the trout population is D) 6,800.
To find the best estimate for the trout population, we can set up a proportion using the ratio of tagged trout to the total number of trout captured.
Let 'x' represent the trout population.
Given:
Tagged trout = 30
Total trout captured = 600
The proportion can be set up as:
Tagged trout / Total trout captured = Marked trout / Total trout population
30 / 600 = 340 / x
Now, we can cross multiply:
30x = 600 * 340
Divide both sides of the equation by 30:
x = (600 * 340) / 30
x = 6800
Therefore, the best estimate for the trout population is 6,800.
So, the correct answer is option D: 6,800.
To find the best estimate for the trout population, we can use a proportion based on the ratio of tagged trout to the total number of captured trout.
The ratio of tagged trout to the total trout population is given by:
(30 tagged trout) / (600 captured trout) = (340 tagged trout) / (x total trout population)
To solve for x, the total trout population, we can cross multiply:
30 * x = 340 * 600
This gives us:
30x = 204,000
Divide both sides by 30:
x = 204,000 / 30
The best estimate for the trout population is approximately 6,800.
Therefore, the correct answer is D) 6,800.