SOLUTION 6: Begin with the function
$$f(x)= e^{-x}$$
and choose
$$x-values: 0 \rightarrow 0.3$$
so that
$$\Delta x = 0.3-0 = 0.3$$
The derivative of $\ y=f(x) \$ is
$$f'(x)= e^{-x} (-1) = -e^{-x}$$
The exact change of $y-$values is
$$\Delta y = f(0.3) - f(0)$$ $$= e^{-0.3} - e^{0}$$ $$= e^{-0.3} - 1$$
The Differential is
$$dy = f'(0) \ \Delta x$$ $$= -e^{0} \cdot (0.3)$$ $$= (-1) (0.3)$$ $$= -0.3$$
We will assume that
$$\Delta y \approx dy \ \ \ \ \longrightarrow$$ $$e^{-0.3} - 1 \approx -0.3 \ \ \ \ \longrightarrow$$ $$e^{-0.3} \approx 1 - 0.3 \ \ \ \ \longrightarrow$$ $$e^{-0.3} \approx 0.7$$

NOTE: The number 0 was chosen for its proximity to 0.3 and for it's convenient exponential value. Check the accuracy of the final estimate using a CALCULATOR: $e^{-0.3} \approx 0.7408$