y is directly proportional to the cube root of x. if x is increased by 200%, find the % increase of y.
1 answer:
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}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx%7D)
if x is increased by 200%, then
old x - 100%
new X - 300%
hence,

and new Y is
![Y=\sqrt[3]{X}=\sqrt[3]{3x}](https://tex.z-dn.net/?f=Y%3D%5Csqrt%5B3%5D%7BX%7D%3D%5Csqrt%5B3%5D%7B3x%7D)
![Y=\sqrt[3]{3}y](https://tex.z-dn.net/?f=Y%3D%5Csqrt%5B3%5D%7B3%7Dy)
Thus,
y - 100%
Y - a%
Then

![\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\%](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7B%5Csqrt%5B3%5D%7B3%7D%20y%7D%3D%5Cdfrac%7B100%7D%7Ba%7D%5C%5C%20%5C%5C%5Cdfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B3%7D%7D%3D%5Cdfrac%7B100%7D%7Ba%7D%5C%5C%20%5C%5Ca%3D100%5Csqrt%5B3%5D%7B3%7D%5Capprox%20%20144.22%5C%25)
y increases by 44.22%
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