5.16 Euler's methodIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.16 Euler's method

1. A function $y$ satisfies $\frac{dy}{dx}=2x-y$, with $y=3$ when $x=0$. Euler's method with step length $h=0.5$ is used to approximate $y$.
   Find the approximation to $y$ when $x=1.5$.2 marks
2. The temperature $T\,^\circ$C of a cup of tea, $t$ minutes after it is poured, satisfies $\frac{dT}{dt}=-0.1(T-20)$, and $T=90$ when $t=0$. Euler's method with step length $h=2$ minutes is used to estimate $T$.
   Continue the method to estimate $T$ when $t=6$.2 marks
3. The number of fish $P$ in a lake, $t$ years after the lake is stocked, is modelled by $\frac{dP}{dt}=0.4P\left(1-\frac{P}{500}\right)$, with $P=100$ when $t=0$. Euler's method with step length $h=1$ year is used. A GDC or spreadsheet may be used.
   Use Euler's method to estimate the number of fish after 1 year and after 2 years.3 marks