A female moth lays nearly 150 eggs. In on year there may live up to five generations. Each larva eats about 20mg of wool. Assume that 2/3 of the eggs die and that 50% of the remaining moths are females. Estimate the amount of wool that may be destroyed b the descendants of one female within a year. (The first female belongs to the first generation)
To estimate the amount of wool that may be destroyed by the descendants of one female moth within a year, we need to break down the problem into several steps:
Step 1: Calculate the number of female moths in each generation.
- Start with the assumption that the female moth lays nearly 150 eggs.
- Given that 2/3 of the eggs die, we can calculate the number of surviving eggs: 150 * (1 - 2/3) = 50 eggs.
- Assuming that 50% of the remaining moths are females, the number of female moths in each generation will be: 50 * 0.5 = 25 female moths.
Step 2: Calculate the number of generations in one year.
- The problem states that there can be up to five generations in one year.
Step 3: Calculate the total number of female moths in all generations within a year.
- Since there can be up to five generations in one year, the total number of female moths in all generations will be: 25 (female moths per generation) * 5 (generations) = 125 female moths.
Step 4: Calculate the total amount of wool eaten by the descendants of one female within a year.
- Assuming each larva eats about 20mg of wool, the total amount of wool eaten by one generation will be: 20mg * 25 female moths = 500mg.
- Since there can be up to five generations in one year, the total amount of wool eaten by the descendants of one female within a year will be: 500mg * 5 (generations) = 2500mg or 2.5 grams of wool.
Therefore, the descendants of one female moth may potentially destroy approximately 2.5 grams of wool within a year.