(i)[6]
Set up a differential equation involving $y$ and $t$, and solve it.
(ii)[2]
Determine the exact value that the mass of $B$ tends to as $t$ becomes large. State what occurs to the mass of $A$ as $t$ becomes large.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
In a certain chemical process, substance $A$ reacts with substance $B$ and reduces it. If the masses of $A$ and $B$ at time $t$ after the process begins are $x$ and $y$ respectively, it is given that $\frac{dy}{dt} = -0.2xy$ and $x = \frac{10}{(1+t)^2}$. At the start of the process, $y = 100$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $\dfrac{dy}{dt}=-\dfrac{2y}{(1+t)^2}$ or an equivalent form” …
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