Still unsure of how to find the inflection points with an e^x problem...

Take this problem:

f(t) = 1 - e^-0.03t

f'(t) = -e^-.03t + (-.03t)

f'(t) = -0.03te^-0.03t

It seems logical that if t=0 then f'(t) =0, but is there a way to solve it without guessing?

f"(t) = -.03t(e^-.03t)(-.03)

f"(t) = .0009te^-.03t

In other words, can you set .0009t = e^-.03t and solve? or do you just pick some points near 0 and plot?