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 can break down the problem into smaller steps.

Step 1: Calculate the number of eggs that survive.
Start with the initial 150 eggs laid by the female moth. We know that 2/3 of these eggs die, so we need to find (1/3) * 150 = 50 eggs that survive.

Step 2: Calculate the number of female moths from the surviving eggs.
Since we are assuming that 50% of the remaining moths are female, we calculate (50/100) * 50 = 25 female moths.

Step 3: Calculate the total number of eggs laid by the 25 female moths.
Each female moth lays nearly 150 eggs, so the total number of eggs laid by the 25 female moths is 150 * 25 = 3750 eggs.

Step 4: Calculate the number of eggs that survive from the 3750 eggs.
Following the same assumption that 2/3 of the eggs die, we can find (1/3) * 3750 = 1250 eggs that survive.

Step 5: Calculate the number of female moths from the surviving eggs.
Using the assumption that 50% of the remaining moths are female, we calculate (50/100) * 1250 = 625 female moths.

Step 6: Repeat Steps 3-5 for each subsequent generation.
Since there may be up to five generations in one year, we repeat Steps 3-5 four more times for a total of five generations.

Step 7: Calculate the total number of female moths over the five generations.
By adding up the number of female moths from each generation, we get 25 + 625 + 15625 + 390625 + 9765625 = 10117125 female moths.

Step 8: Calculate the total amount of wool consumed by the female moths.
Since each larva eats about 20mg of wool, we multiply the total number of female moths by 20mg: 10117125 * 20 = 202,342,500mg of wool.

So, the descendants of one female moth may destroy approximately 202,342,500mg (or 202.34kg) of wool within a year.