Question

If $y=kx^{\frac{1}{4}}$ and $y=3\sqrt{2}$ at $x=81$, what is the value of $y$ at $x=4$?

Answer 1

To determine the value of y at x=4, first calculate the constant k using the initial conditions y=3√2 at x=81, then substitute k and x=4 into the equation y=kx^{¼} to get the result y ∼ 2.82.

Step-by-step explanation:

To find the value of y at x=4, we must first determine the value of k using the given equation and conditions. We know that y=kx^{¼} and at x=81, y=3√2. Let's calculate k.

Substitute x=81 and y=3√2 into the equation:

3√2 = k(81)^{¼}

Since 81 is a perfect fourth power (3^4), the fourth root of 81 is 3. Thus:

3√2 = k(3)

To find k, divide both sides by 3:

k = √2

Now that we have k, we can find y when x=4:

y = (√2)(4)^{¼}

The fourth root of 4 is 2, so this simplifies to:

y = (√2)(2)

And since √2 ∼ 1.41, the approximate value of y is:

y ∼ 2.82.