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'll break down the problem step by step.
Step 1: Calculate the number of female moths in each generation.
Assuming 2/3 of the eggs die:
Number of eggs = 150
Number of surviving eggs = 150 - (2/3) * 150 = 150 - 100 = 50
Assuming 50% of the remaining moths are females:
Number of female moths = 50% * 50 = 0.5 * 50 = 25
Step 2: Calculate the number of generations.
Given that there can be up to five generations in a year.
Step 3: Calculate the total number of female moths in all generations within a year.
Since each generation produces 25 female moths, we'll multiply this number by the total number of generations in a year.
Total number of female moths in a year = 25 * Number of generations
Step 4: Calculate the total number of larvae.
Given that each female moth lays 150 eggs, we'll multiply this number by the total number of female moths in a year.
Total number of larvae = 150 * Total number of female moths in a year
Step 5: Calculate the total amount of wool consumed by the larvae.
Given that each larva eats about 20mg of wool, we'll multiply this number by the total number of larvae.
Total amount of wool consumed = 20mg * Total number of larvae
Finally, to estimate the amount of wool that may be destroyed by the descendants of one female moth within a year, we need to substitute the values we calculated in the previous steps into Step 5.