Given, y varies directly as the cube of x.
So, [tex] y=kx^3 [/tex]
By using the order pair (4, 16) we can get x=4 and y=16.
Now plug in these values in the above equation.
So, 16=k*4^3
16 = k *64
16/64 = k (By dividing each sides by 64).
So, k=1/4
So, the equation for this variation is y= 1/4*x^3
Now we need to find the value of y for x=2.
So, plug in x=2 in the above equation. Hence,
y=1/4* 2^3
=1/4*8
=8/4
=2
So, y=2
