Pierce Crawford
05/26/2024 · Primary School

(c) KNO \( { }_{3} \) dissolves in nethanof; this mass \( x \) grams dissulved at \( t \) seconds satisfies the differential equation \[ \frac{d y}{d t}=-0,004 y^{2}+0,8 y \] (i) What is the max amount of satt that will ever dissolve? (ii) If \( y(0)=50 \mathrm{~g} \), how long will it toke an additional sog to dissolve? lii) Draw a phase line using the equilibrium points and state if they ane Stable or unstable.

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(i) The maximum amount of salt that will ever dissolve is 200 grams. (ii) It will take an infinite amount of time for the solution to reach 200 grams from 50 grams. (iii) The phase line shows that \(y = 0\) is unstable and \(y = 200\) is stable.

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