中四數:反變

(a)
y = 1/x³

當 x = xo，y = yo :
yo = 1/xo³ ...... [1]

當 y = yo(1 - 27.1%) :
yo(1 - 27.1%) = 1/x³
0.729yo = 1/x³ ...... [2]

把 [1] 代入 [2] 中：
0.729(1/xo³) = 1/x³
x³ = xo³(1/0.729)
x = xo(1/0.9)
x = (10/9)xo

x 的百分變化：
{[(10/9)xo - xo]/xo} * 100%
= +(100/9)%
= +(11又1/9)%
(≈ +11.11%)


(b)
y = 1/x³

當 x = xo，y = yo :
yo = 1/xo³ ...... [1]

當 y = yo(1 + 33.1%) :
yo(1 + 33.1%) = 1/x³
1.331yo = 1/x³ ...... [3]

把 [1] 代入 [3] 中：
1.331(1/xo³) = 1/x³
x³ = xo³(1/1.331)
x = xo(1/1.1)
x = (10/11)xo

x 的百分變化：
{[(10/11)xo - xo]/xo} * 100%
= -(1/11)%
= -(9又1/11)%
(≈ -9.09%)

(a)
y=1/x^3
x^3=1/y
x=(1/y)^(1/3)
y的新值=(1-27.1)^(1/3)y=0.9y
x的百分變化=[(1/0.9y)^(1/3)-(1/y)^(1/3)]/(1/y)^(1/3)*100%
x的百分變化=3.57%

(b)
y=1/x^3
x^3=1/y
x=(1/y)^(1/3)
y的新值=(1+33.1%)^(1/3)y=1.1y
x的百分變化=[(1/1.1y)^(1/3)-(1/y)^(1/3)]/(1/y)^(1/3)*100%
x的百分變化=-9.09%