The area of a wetland drops by 1/4 every 8 years. What percent of its total area disappears after 40 years?
Percent lost %?
I would use the formula
amount = (.75)^(40/8)
= .75^4
= .3164
so after 40 years we have 31.64% left
so the percent lost is 68.36 .
Hmmm. 40/8 = 4?
40/8=5
.75^5=0.2373
100-23.73=76.27%
thanks :)
To find the percent of the wetland's total area that disappears after 40 years, we can start by calculating the number of 1/4 decreases that occur over 40 years.
Since the area drops by 1/4 every 8 years, we can divide 40 by 8 to determine the number of 1/4 decreases: 40 / 8 = 5.
This means that after 40 years, the wetland experiences 5 decreases of 1/4 its original area.
To calculate the percent of the total area that disappears, we need to calculate the total decrease as a fraction of the original area.
Each decrease of 1/4 represents 25% of the previous area, so after 1 decrease, the wetland has 100% - 25% = 75% of its original area remaining.
Similarly, after 2 decreases, the wetland has 75% - 25% = 50% of its area remaining.
We can continue this pattern for each of the 5 decreases:
1 decrease: 75% remaining
2 decreases: 50% remaining
3 decreases: 25% remaining
4 decreases: 0% remaining
So, after 40 years, the wetland's area decreases to 0% of its original area.
Therefore, 100% - 0% = 100% of the wetland's total area disappears after 40 years.
Thus, the percentage lost is 100%.