fitting – Finding the best fit: Mathematica vs. Excel

My data is:

data = {{0, 0.05}, {40, 0.079}, {80, 0.113}, {120, 0.18}, {160, 0.31}, {200, 0.5}, {240, 0.71}, {280,0.86}, {320, 1.02}};

With Excel we can fit the data with $0.0548996* e^{0.0099675 x}$ which is more or less good: (blue curve is the fit)

enter image description here

Now, if we try with Mathematica:

FindFit(data, a*E^(b x), {a, b}, x)

it returns: Working precision MachinePrecision is insufficient to achieve the
requested accuracy or precision; ${a -> 2.76357*10^{-76}, b -> 1.}$, which is obviously wrong.

How can one find the best fit with Mathematica for this data?