Variations and variables

Question

Suppose that y is proportional to the 4th power of x, and that y=18 when x=2. What is y when x=5? Round your answer to two decimal places if necessary.

y=???

Can someone solve this for me and show the steps? Thank you!

Answer 1

"Y is proportional to the 4th power of x" means:

y = kx⁴

Hence y/x⁴ = k. This is true for any ordered pair (x,y) on the graph. So we can set up a proportion for the two points (2,18) and (5,y):

18/2⁴ = y/5⁴

Solve for y.