Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
In one chemical reaction, substance $A$ reacts with substance $B$. At $t$ seconds after the process begins, the masses in grams of $A$ and $B$ are $x$ and $y$ respectively. It is stated that $\frac{dy}{dt} = -0.6xy$ and $x = 5e^{-3t}$. When $t = 0$, $y = 70$.
(i)[6]
Set up a differential equation in $y$ and $t$. Then solve it and give $y$ as a function of $t$.
(ii)[2]
Let $p$ represent the percentage of the original mass of $B$ that remains at time $t$. Determine the exact value that $p$ tends to as $t$ becomes very large.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Insert the expression for $x$, separate the variables correctly and make an attempt to integrate both sides.” …