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:

$$ y = 20\ \boldsymbol{e}^{-{x\over2}} -20\ \boldsymbol{e}^{2x\over 5}+2 x\ \boldsymbol{e}^{-{x\over2}}$$

$$ y = \boldsymbol{e}^{-3x} + 3x\ \boldsymbol{e}^{-3x} + 25x^2\ \boldsymbol{e}^{-3x}$$

  • $\begingroup$ the 1st example you give is "out-of-shape" vs, the question you pose (why $e^{2x/5}$ ?) $\endgroup$ – G Cab Oct 29 '16 at 14:32
  • $\begingroup$ @GCab The coefficient $c_i$ of $x$ in $e^{c_ix}$ may vary in each term. $\endgroup$ – Eana Hufwe Oct 29 '16 at 23:11

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