Probability approximation. At which t is this approximation invalid?

Question

Could someone help me with this exercise: Probability P of mutation: P(t) = 1 - exp(-at). Approximate P(t) for small a. At which t is this approximation invalid? (I tried the Taylor expansion, but am stuck. This is what i got for the Taylor exp: https://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=f9476968629e1163bd4a3ba839d60925&title=Taylor%20Series&theme=blue&i0=1-e%5E(-x*t)&i1=x&i2=0&i3=3&podSelect=&showAssumptions=1&showWarnings=1)