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Suppose that y is inversely proportional to the 4th power of x, and that y=16 when x=6. What is y when x=3? Round your answer to two decimal places if necessary.

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Answer:

y = 1

Step-by-step explanation:

Given

  • y ∝ x⁴

⇒ y = kx⁴

Finding the proportionality constant, k

  • y = 16 and x = 3
  • 16 = k (6)⁴
  • 16 = 1296k
  • k = 16/1296
  • k = 1/81

Finding y

  • y = 1/81 x (3)⁴
  • y = 1/81 x (81)
  • y = 1

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