variations and variables

Question

Suppose that y is inversely proportional to the 4th power of x, and that y=15 when x=6. What is y when x=5?

y=???

Answer 1

Since the two are inversely proportional, we set it up as follows:

x⁴ y = k

Then plug in what x and y equal.

6⁴•15 = k

1296 • 15 = k

k = 19440

Then plug in 5 for x and 19440 for k, in x⁴y = k

5⁴y = 19440

625 • y = 19440

y = 19440 / 625

y = 31.104

Answer 2

y = k / x⁴ for some constant, k

Since y = 15 when x = 6, we have 15 = k / 1296. So, k = 19440.

y = 19440 / x⁴

Therefore, when x = 5, y = 19440 / 5⁴ = 31.104