Problem 3 - Biology: The Dynamic Science

Question

One day you caught and marked 90 butterflies in a population. A week later, you returned to the population and caught 80 butterflies, including 16 that had been marked previously. What is the size of the butterfly population? a. 170 b. 450 C. 154 d. 186 e. 106

Step-by-Step Solution

Answer

The size of the butterfly population is estimated to be 450.

Step 1: Understand the Problem

A total of 90 butterflies were marked and released. Then 80 were caught, including 16 that were previously marked. Use the proportion of the marked butterflies recaptured to estimate the size of the entire butterfly population.

Step 2: Set Up the Proportion

The proportion can be set up as follows: \( \frac{Marked \space butterflies \space from \space first \space catch}{estimated \space total \space population} = \frac{marked \space butterflies \space from \space second \space catch}{total \space butterflies \space from \space second \space catch} \)

Step 3: Insert the Values

Insert the given values into the proportion: \( \frac{90}{x} = \frac{16}{80} \)

Step 4: Solve for the Unknown

By cross-multiplication, 80 * 90 = x * 16, hence, x = \( \frac{80*90}{16} = 450\)