When might a plot of ln[a] vs time not yield a straight line?

Considering a reaction:

A → B

The rate equation may be described as:

r = - k[A]ⁿ

Taking the natural log,

ln (r) = - nln ([A]) + ln (k)

Therefore, the only time the graph of ln[A] vs time will be a straight line is when the order of the reaction is 0, meaning the reaction is independent of reactant concentration.