(1) ...n = ke (-at) (mathematical formula), as before, let's look at its units. N is dimensionless, so k must be dimensionless. We can also conclude that the unit of A is the reciprocal of the unit of time.
(2) Note that we have no special reason to use the half-life or the series of E or anything else. As long as the formula of 1.7 holds, these formulas are completely equivalent: