index number

不好意思，不知放哪里，只好放在这里。
explain what I1985/1983=98 means
1985/1983是在I 下面的。

2.The following data gives the consumer price index from year 1999 to 2004.

	Year	Consumer Price Index (Base year = 1995)	Consumer Price Index (Base year = 2001)
	1999 2000 2001 2002 2003 2004	103.5 108.0 112.5 X	Y 96 100.0 108.0 110.2 101.4

(i). What is the CPI for year 2002 calculated using year 1995 as the base year
[i.e.the value of X] Answer: 121.5

(ii) What is the CPI for year 1999 calculated using year 2001 as the base year
[i.e. the value of Y] Answer: 92.0

(iii) Construct another index using year 2000 as the base year.

不好意思。
你的问题是什么？

我的确已经找出
i) x = 121.5
和
ii) y = 92.0

你的

I1985/1983=98

是如何写的？

是
(1985 I) / 1983 = 98

还是
1985 / (1983 I) = 98

还是
(1983 I) / 1985 = 98



你的真真问题是什么？
I是不是代表Index?

1. (b) Explain
what I_1985/1983 = 98 means.
2.请问怎么找Y？（iii）怎么做？

1. (b) Explain
what I_1985/1983 = 98 means.

应该是这样子写吧？

The CPI for year 1985 calculated using year 1983 as the base year is 98.

你认为呢？


2.请问怎么找Y？（iii）怎么做？

Let
a = 1999
b = 2000
c = 2001
d = 2002
e = 2003

f = 1995


a/f x 100% = 103.5 % -------- (1)

b/f x 100% = 108.0% ----------- (2)

c/f x 100% = 112.5% ---------- (3)

d/f x 100% = x ------------------- (4)

a/c x 100% = y ------------------ (5)

b/c x 100% = 96% --------------- (6)

d/c x 100% = 108.0% ------------(7)

e/c x 100% = 110.2% ------------ (

g/c x 100% = 101.4% ------------- (9)


Form (1) and (5),
103.5 % f = c y ------------- (10)

Form (2) and (6),
108% f = 96% c ------------- (11)

Form (4) and (7),
f x = 108.0% c -------------- (12)

From (11),
c = 108 f /96 --------------- (13)


Substitute (13) into (10),
103.5 % f = c y
103.5 % f = (108 f /96) y
...
y = 92%


Substitute (13) into (12)
f x = 108.0% c
f x = 108.0% (108 f /96)
...
x = 1.215%

谢谢！
(iii) Construct another index using year 2000 as the base year.怎么做？

我星期六才帮你看看如何解你的问题好吗？因为weekdays我正忙着工作。
其他数学爱好者可以去试一试解。

目前的想法应该要找出1999至2004年、1995和2000年的未知数才可以解以上的问题，我还没去试。这是我的assumption.

关于I 和II, 我认为用chain rule的method 也可以做得到。