Question

y is directly proportional to the cube root of x. if x is increased by 200%, find the % increase of y.

Answer 1

y increases by 44.22%

Explanation:

If y is directly proportional to cube root of x, then y can be written as

`y=\sqrt[3]{x}`

if x is increased by 200%, then

old x - 100%

new X - 300%

hence,

`(x)/(X)=(100)/(300)\\ \\X=3x`

and new Y is

`Y=\sqrt[3]{X}=\sqrt[3]{3x}`

`Y=\sqrt[3]{3}y`

Thus,

y - 100%

Y - a%

Then

`(y)/(Y)=(100)/(a)`

`\frac{y}{\sqrt[3]{3} y}=(100)/(a)\\ \\\frac{1}{\sqrt[3]{3}}=(100)/(a)\\ \\a=100\sqrt[3]{3}\approx 144.22\%`

y increases by 44.22%