Question

britney keeps track of the populations of various creatures near a lake. in order to estimate the dragonfly population, she captures 1,400 dragonflies and marks them with special paint. she releases them, waits a few days, and then captures 620 dragonflies. she notices that 62 of these dragonflies are marked. to the nearest whole number, what is the best estimate for the dragonfly population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. The ratio of marked dragonflies in the recapture should equal the ratio of marked dragonflies to total population:
$$\frac{62}{620} = \frac{1400}{N}$$

Step2: Simplify left fraction

Simplify $\frac{62}{620}$ to $\frac{1}{10}$:
$$\frac{1}{10} = \frac{1400}{N}$$

Step3: Solve for $N$

Cross-multiply to isolate $N$:
$$N = 1400 \times 10$$
$$N = 14000$$

Answer:

14000