Arturo O. answered • 03/13/18

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dN/dt = -λN

is correct, then the 1st equation

−λ△t= (N(t+△t)−N(t)) / (△t)

CANNOT be correct. λ must have units of time

^{-1}, so the left side of the 1st equation is dimensionless. The right side has units of amount/time. The left and right sides are different physical quantities. They cannot be equal.