Question 1015193
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Close, but you have a sign error.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\text{d}}{\text{d}t}\,10000e^{-0.01t}\ =\ -100e^{-0.01t}]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y'(3)\ =\ -100e^{-0.03}\ \approx\ -97.0]


Exponential decay is decreasing function.  A function is decreasing in any interval where the first derivative is negative.  The derivative of *[tex \Large e^{\alpha x}] is negative over the entire domain of the function whenever *[tex \Large \alpha\ <\ 0]


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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