Respuesta :
[tex]y\text{ = }\frac{2^5}{x^4}^{}[/tex]Explanation:
We rewrite the staement into a methematical expression:
[tex]\begin{gathered} y\text{ }\propto\text{ }\frac{1}{fourth\text{ opower of x}} \\ \text{where }\propto\text{ represents varies} \\ fourth\text{ power of x }=x^4 \\ \\ y\text{ }\propto\text{ }\frac{1}{x^4} \\ \text{removing the varies symbol i to an equation:} \\ \text{The equation beomes:} \\ y\text{ = k}\frac{1}{x^4} \\ \text{where k = constant of proportion} \end{gathered}[/tex][tex]\begin{gathered} to\text{ get the alue of k, we substitute for x and y in the equation we got above:} \\ \text{when x = 2, y = 2} \\ y\text{ = k}\frac{1}{x^4} \\ 2\text{ = k}\frac{1}{2^4} \\ 2\text{ = }\frac{k}{2^4} \end{gathered}[/tex][tex]\begin{gathered} 2\times(2^4)\text{ = k} \\ k=2^1\times2^4=2^{+4} \\ k=2^5 \end{gathered}[/tex]The equation describing the relationship between the variables:
[tex]\begin{gathered} y=2^5\frac{1}{x^4} \\ y\text{ = }\frac{2^5}{x^4}^{} \end{gathered}[/tex]