DSE Maths-Core IV: Variations變分

題目: z = k * x^2 / y^3

比x,y,z你叫你搵個k出黎..呢d就好簡單,要教既係百分比轉變(percentage change)
如: x上升20%, y下降30%, 咁z變幾多?

做法: z' (即係新既z) = k * ( x * (1+20%) )^2 / ( y * (1+30%) )^3

z' = k * (1.2x)^2 / (1.3y)^3

z' = k * 1.44x^2 / 2.197y^3

z' = k * x^2 / y^3 * 1.44 / 2.197   (將原本z既部分擺埋一齊,另外既數字擺埋一齊)

z' = z * 1.44 / 2.197

z' = z * 0.6554

z' = z * ( 1 - 0.3446 )                 (要變做1+或者1-,後面個數先係百分比轉變)

答案就係..z減少左34.46%
書好多時都教 ( 新 - 舊 ) / 舊 * 100%..咁有d多餘..因為咁做都係要搵個原本既z約走佢,用上面個方法就方便d

eg2. z = k * x^1/2 / y ^2
x increases 44%, y decrease 25%, z % change?
做法: z' = k * (1.44x)^1/2 / (0.75y)^2
z' = k * 1.2x^1/2 / 0.5625y^2
z' = z * 1.2 / 0.5625
z' = z * 2.1333
z' = z * (1+1.1333)
so z increases 113.33%

eg3. z = k * x^1/2 / y ^2
x increase 44%, z decrease 25%, y % change?
首先要轉主項(subject)做y..之後做法同上~唔多講了~