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
[tex]y=\sqrt[3]{x}[/tex]
if x is increased by 200%, then
old x - 100%
new X - 300%
hence,
[tex]\dfrac{x}{X}=\dfrac{100}{300}\\ \\X=3x[/tex]
and new Y is
[tex]Y=\sqrt[3]{X}=\sqrt[3]{3x}[/tex]
[tex]Y=\sqrt[3]{3}y[/tex]
Thus,
y - 100%
Y - a%
Then
[tex]\dfrac{y}{Y}=\dfrac{100}{a}[/tex]
[tex]\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\%[/tex]
y increases by 44.22%
