(a(i))[1]
State why $\frac{dx}{dt} = k(50 - x)$, where $k$ is a constant.
(a(ii))[8]
Given that $x = 0$ when $t = 0$, and $x = 25$ when $t = 10$, solve the differential equation in part (i) and write $x$ as a function of $t$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
During a particular chemical reaction, compound $A$ is produced from compound $B$. At time $t$ after the reaction begins, the masses of $A$ and $B$ are $x$ and $y$ respectively, and their total mass stays at $50$ for the whole reaction. At any moment, the rate at which the mass of $A$ increases is proportional to the mass of $B$ at that moment.