The profit of a company had been decreasing by 10% every year from 1999 to 2003. In 2004, the profit had increased by 50%. So the directors thought that the profit had returned to the level in 1998. Do you think they were correct? Why?
P.S:請各位數學奇才幫幫手啦!!!!!!!!!!!
怎樣可以清楚寫出step?
2007-01-03 7:16 pm
回答 (4)
2007-01-03 7:29 pm
✔ 最佳答案
Let the profit made in 1998 be $yIn 2003, profit is:
y ( 1-10%)( 1-10%)( 1-10%)( 1-10%)( 1-10%)
=y x 0.9^5
=0.59049y
In 2004, the profit is:
0.59049y (1+50%)
=0.59049x1.5 y
=0.885735y
not equal to y
So, he is not correct.
2007-01-03 7:38 pm
Let the profit in 1998 be $x
The profit gain in 2003 will be = x [ (1-10%)^5] ( "^" = 次方 )
the profit gain in 2004 = x [ (1-10%)^5] (1+50%)
= 0.89 x
The profit gain in 2004 is only 89% of the level in 1998.
Therefore the directors are not correct.
The profit gain in 2003 will be = x [ (1-10%)^5] ( "^" = 次方 )
the profit gain in 2004 = x [ (1-10%)^5] (1+50%)
= 0.89 x
The profit gain in 2004 is only 89% of the level in 1998.
Therefore the directors are not correct.
2007-01-03 7:36 pm
Profit x 0.9^5 x 1.5
= Profit x 0.59049 x 1.5
= Profit x 0.885735
-> Less than 1998 Profit!
The directors are wrong since 2004 Profit is less than 1998 by decreasing 11.5% as a whole.
1999 to 2003 equals 5yrs
so, 0.9^5 (decrease 10% each yr)
increase 50% = 1.5
Thanks!
= Profit x 0.59049 x 1.5
= Profit x 0.885735
-> Less than 1998 Profit!
The directors are wrong since 2004 Profit is less than 1998 by decreasing 11.5% as a whole.
1999 to 2003 equals 5yrs
so, 0.9^5 (decrease 10% each yr)
increase 50% = 1.5
Thanks!
參考: myself
2007-01-03 7:32 pm
我可以用中文答嗎?
其實 你應該已猜到不可能相等
因為佢減少以複利息 講多無謂 行動最實際
設係1999年初既profit為x
2003年尾的profit則為=x乘(0.9)既五次方
係2004年尾profit則為=2003年尾的profit乘(1.5)
=x乘0.885(準確至三位有效數字)不等於1999年profit
其實 你應該已猜到不可能相等
因為佢減少以複利息 講多無謂 行動最實際
設係1999年初既profit為x
2003年尾的profit則為=x乘(0.9)既五次方
係2004年尾profit則為=2003年尾的profit乘(1.5)
=x乘0.885(準確至三位有效數字)不等於1999年profit
收錄日期: 2021-04-12 17:44:40
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070103000051KK00967