Question

scientists tagged 770 pike for a research project about a local lake. later, they trapped 270 pike, of which 21 had tags. to the nearest whole number, what is the best estimate for the pike population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. $\frac{\text{Tagged total}}{\text{Total population}} = \frac{\text{Tagged recaptured}}{\text{Recaptured total}}$
$\frac{770}{N} = \frac{21}{270}$

Step2: Solve for $N$

Cross-multiply: $21N = 770 \times 270$
$21N = 207900$
$N = \frac{207900}{21}$

Step3: Calculate final value

$N = 9900$
Wait, correction:

Step1: Set up mark-recapture proportion

$\frac{770}{N} = \frac{21}{270}$

Step2: Cross multiply to isolate $N$

$N = \frac{770 \times 270}{21}$

Step3: Compute the value

First simplify $\frac{270}{21} = \frac{90}{7}$
$N = 770 \times \frac{90}{7} = 110 \times 90 = 9900$

Step1: Define mark-recapture ratio

Let $N$ = total pike population. The ratio of tagged pike to total population equals the ratio of tagged recaptured pike to total recaptured pike:
$\frac{770}{N} = \frac{21}{270}$

Step2: Rearrange to solve for $N$

Cross-multiply to isolate $N$:
$N = \frac{770 \times 270}{21}$

Step3: Calculate the result

Simplify and compute:
$N = \frac{770 \times 270}{21} = 770 \times 12.8571 \approx 9900$

Answer:

9343