(i)[1]
Show that $N$ and $t$ satisfy $\frac{dN}{dt} = -0.01e^{-0.02t}N$.
(ii)[6]
Solve the differential equation and determine $t$ when $N = 800$.
(iii)[1]
State how $N$ behaves when $t$ becomes very large.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
Let $N$ denote the number of insects $t$ weeks after observations begin. The population is falling at a rate proportional to $Ne^{-0.02t}$. Both $N$ and $t$ are continuous variables, and when $t = 0$, $N = 1000$ and $\frac{dN}{dt} = -10$.