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Solve the given problems.The reliability $R(0 \leq R \leq 1)$ of a certain computer system is given by $R=e^{-0.0002 t},$ where $t$ is the time of operation (in h). Find $d R / d t$ for $t=1000 \mathrm{h}$.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

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Okay, this girl question has some application led to it, but essentially were given an equation which is R equals either the negative zero point three zeros to T. And we're asked to find the odd ET when T equals 1000. So take the derivative and substitute in 1000. Is basically are two jobs here. Quite a simple problem. Once we strip the application layer off of this, so taking the derivative of this function, we get the core fishing with T down in front and then we're gonna substitute this value that were given in and I can eat at the negative 0.2 times 1000. Okay, we can go to our calculator here for this to get an estimate. If we want, make sure we get enough zeros in there and then either the parent negative three zeros times amazon. And here is our it's a negative 1.64 times 10 to the minus four. Or you could say this is three zeros 164 And then the units here are put out. Pretty simple problem. Once we get the application layer out of the way

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