(a)[5]
Solve the differential equation to obtain a relationship between $x$, $t$ and $k$.
(b)[3]
If $x = 40$ when $t = 10$, determine the value of $k$ and the value that $x$ approaches as $t$ becomes large.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
In one chemical reaction, the quantity, $x$ grams, of a substance is rising. The differential equation linking $x$ and $t$, where $t$ is the time in seconds from the start of the reaction, is $\frac{dx}{dt} = kx e^{-0.1t}$, with $k$ a positive constant. It is also stated that $x = 20$ at the beginning of the reaction.