Use a linear approximation (or differentials) to estimate the given number.?

Find the equation of the tangent line to the graph of the function f(x) = e^x at a convenient point (something close to x = 0). Then the tangent line will look very much like f(x) in that area, so you can evaluate the tangent line at x =- 0.01 and not bother with evaluating e^-0.01.