How to:
- Determine the shape of,
- and sketch the curve (Only x/y axis intercept points are required for labeling)
for equations in the format of:
$$f(x) = a_1x^{b_1}\boldsymbol{e}^{c_1 x} +\ ...\ + a_nx^{b_n}\boldsymbol{e}^{c_n x}$$
where $a_i \neq 0$, $b_i, c_i \in \mathbb{R}$.
Some examples of such equation:
$$ y = 20\ \boldsymbol{e}^{-{x\over2}} -20\ \boldsymbol{e}^{2x\over 5}+2 x\ \boldsymbol{e}^{-{x\over2}}$$
$$ y = \boldsymbol{e}^{-3x} + 3x\ \boldsymbol{e}^{-3x} + 25x^2\ \boldsymbol{e}^{-3x}$$