Question

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

Answer 1

Answer:

y increases by 44.22%

Step-by-step 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,

$\dfrac{x}{X}=\dfrac{100}{300}\\ \\X=3x$

and new Y is

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

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

Thus,

y - 100%

Y - a%

Then

$\dfrac{y}{Y}=\dfrac{100}{a}$

$\dfrac{y}{\sqrt[3]{3} y}=\dfrac{100}{a}\\ \\\dfrac{1}{\sqrt[3]{3}}=\dfrac{100}{a}\\ \\a=100\sqrt[3]{3}\approx 144.22\%$

y increases by 44.22%