The problem and its solution are attached as TheProblemAndSolution.jpg.
2. Relevant equation
ν = L di/dt
The Attempt at a Solution
I don't understand how the solution gets i = 10.0 A for t = 2 ms as well as to how it gets i = 30 – (10 * 10^3) t) (A) for 2 ms < t < 4 ms. More specifically, I see that the equation when 0 < t < 2 ms has i = 10.0 A if one plugs in 2 ms in the t variable like so, 5 * 10^3 (2 * 10^(-3) s) = 10.0 A. However, what I do not get is, why does the equation for the interval (0, 2) work for the point t = 2 ms (does the reasoning relate to the fact that 1.9999 (periodic 9) can be proved to equal 2? As to when 2 < t < 4, something seems off with the first equality but I cannot figure out exactly what. Just to note, I don't see anything wrong with Fig. 2-12 and the way it relates to the equations in the work so I don't think anything is wrong but, to reiterate, I don't get why i = 10.0 A at t = 2 ms and I'm confused as to how to get the equation for when 2 ms < t < 4 ms because the first equality is messed up which throws me off for the rest of the work.
Any help in understanding these things would be greatly appreciated!