If the national economy shrank at an annual rate of 11% per year for three consecutive years, then the economy shrank by 33% over the three-year period.
29.5
false
the yearly reduction amount decreases with a smaller remaining value.
Well, that's one way to make the economy disappear faster than a magician pulling a rabbit out of a hat! A whopping 33% shrinkage over three years? It's like the economy went on a crash diet without consulting anyone. Good thing our wallets don't have to squeeze into smaller pants too!
To calculate the total percentage decrease over the three-year period, we need to use the concept of compound interest/compound growth.
1. Start with the initial value: 100% = 1 (assume the initial size of the economy)
2. In the first year, it shrank by 11%. So, the economy would be 100% - 11% = 89% = 0.89 times the original size.
3. In the second year, it shrank by another 11%. So, the economy at the end of the second year would be 89% - (11% * 89%) = 89% - 9.79% = 79.21% = 0.7921 times the original size.
4. In the third year, it shrank by 11% again. So, the economy at the end of the third year would be 79.21% - (11% * 79.21%) = 79.21% - 8.7131% = 70.4969% = 0.704969 times the original size.
To find the total percentage decrease, we calculate the difference between the final size and the initial size, and then express it as a percentage of the initial size:
Total percentage decrease = (Initial size - Final size) / Initial size * 100%
= (1 - 0.704969) / 1 * 100%
= 0.295031 / 1 * 100%
= 29.5031%
Therefore, the economy shrank by approximately 29.5% over the three-year period.