
The following steps will guide you in calculating the Forward Euler approximation after one step of size $\Delta t = 3.3$, yielding an estimate of $u(3.3)$.
What is the initial condition? $u(0) = $
Based on that result and the differential equation, what is the slope of $u(t)$ at time $t=0$?
$\diff{ u }{t}(0) = 0.3 \left( \frac{1}{790} u{\left (0 \right )} + 1\right) u{\left (0 \right )} =$
Those two numbers are enough information to make a linear approximation at $t=0$.
$L(t) = u(0) + \diff{ u }{t}(0) (t0) =$
We use this linear approximation to approximate the value of $u(t)$ at $t=\Delta t = 3.3$.
$u(3.3) \approx L(3.3) =$

The following steps will guide you in calculating the Forward Euler approximation after the second step of size $\Delta t = 3.3$, yielding an estimate of $u(6.6)$.
Given the value of $u(3.3)$ estimated above and the differential equation, what is the slope of $u(t)$ at time $t=\Delta t = 3.3$?
$\diff{ u }{t}(3.3) = 0.3 \left( \frac{1}{790} u{\left (3.3 \right )} + 1\right) u{\left (3.3 \right )} =$
Those two numbers are enough information to make a linear approximation at $t=\Delta t = 3.3$.
$L(t) = u(3.3) + \diff{ u }{t}(3.3) (t3.3) =$
We use this linear approximation to approximate the value of $u(t)$ at $t=2\Delta t = 6.6$.
$u(6.6) \approx L(6.6) =$

The following steps will guide you in calculating the Forward Euler approximation after the third step of size $\Delta t = 3.3$, yielding an estimate of $u(9.9)$.
Given the value of $u(6.6)$ estimated above and the differential equation, what is the slope of $u(t)$ at time $t=2\Delta t = 6.6$?
$\diff{ u }{t}(6.6) = 0.3 \left( \frac{1}{790} u{\left (6.6 \right )} + 1\right) u{\left (6.6 \right )} =$
Those two numbers are enough information to make a linear approximation at $t=2\Delta t = 6.6$.
$L(t) = u(6.6) + \diff{ u }{t}(6.6) (t6.6) =$
We use this linear approximation to approximate the value of $u(t)$ at $t=3\Delta t = 9.9$.
$u(9.9) \approx L(9.9) =$