Question

while doing research on a local river, a scientist put tags on 210 rainbow trout. later, the scientist captured 200 rainbow trout, of which 12 had tags. to the nearest whole number, what is the best estimate for the rainbow trout population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. The ratio of tagged trout in sample equals ratio of tagged trout in population:
$$\frac{12}{200} = \frac{210}{N}$$

Step2: Cross-multiply to solve for $N$

$$12N = 210 \times 200$$
$$12N = 42000$$

Step3: Isolate $N$

$$N = \frac{42000}{12}$$
$$N = 3500$$

Answer:

3500