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The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
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To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
Given that the probability <span>is
modeled by the function
![y=3(257,959)^x[tex] where x is the impurity concentration and y, given as a percent, is the probability of the fuse malfunctioning.\\Then, the probability of the fuse malfunctioning for an impurity concentration of 0.17 is given by [tex]y=3(257,959)^{0.17}=3(8.316941)=24.95](https://tex.z-dn.net/?f=y%3D3%28257%2C959%29%5Ex%5Btex%5D%20%20where%20x%20is%20the%20impurity%20%0Aconcentration%20and%20y%2C%20given%20as%20a%20percent%2C%20is%20the%20probability%20of%20the%20fuse%20%0Amalfunctioning.%5C%5CThen%2C%20the%20%3C%2Fspan%3Eprobability%20of%20the%20fuse%20malfunctioning%20for%20an%20impurity%20concentration%20of%200.17%20is%20given%20by%20%5Btex%5Dy%3D3%28257%2C959%29%5E%7B0.17%7D%3D3%288.316941%29%3D24.95)
Therefore, the <span>probability of the fuse malfunctioning for an impurity concentration of 0.17 is 25% to the nearest percent.</span>
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Therefore, the <span>probability of the fuse malfunctioning for an impurity concentration of 0.17 is 25% to the nearest percent.</span>
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