Question 618084
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1. Always positive

2. Asymptotic to the x-axis

3. Gets big very fast

4. *[tex \LARGE x(t)\ =\ ab^{\frac{t}{\tau}}] has an *[tex \LARGE x(t)] intercept at *[tex \LARGE (0,a)]

Exponential growth:


*[tex \LARGE \tau\ >\ 0] and *[tex \LARGE b\ >\ 1].  Starts very small at a large magnitude negative number, passes through *[tex \LARGE (0,a)], and then quickly increases without bound.


Exponential decay:


*[tex \LARGE \tau\ <\ 0] and *[tex \LARGE 0\ <\ b\ <\ 1].  Starts very large on the left of the *[tex \LARGE y]-axis, decreases until it passes through *[tex \LARGE (0,a)], and then then decreases until asymptotic to the positive *[tex \LARGE x]-axis.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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