Linearizing an expression involving exponentials

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How can I linearize $f(x) = A(1-\text{exp}(Bx))$? I tried to take the natural logaritm, but could not find something that looks like linear. I am trying to find a fitting curve for this by hand. $A$ and $B$ are real constants.

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For linearizing any function $f(x)$ about a point $x_0$, use: $$f(x)=f(x_0)+(x-x_0)\frac{df}{dx}(x_0)$$ But beware: this approximation works only for points close to $x_0$