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Solve the given problems by finding the appropriate derivative.The power supply $P(\text { in } W$ ) in a satellite is $P=100 e^{-0.005 t}$, where $t$ is measured in days. Find the time rate of change of power after 100 days.

$-0.303 \mathrm{W} / \mathrm{day}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

Derivatives

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So we need to find the time rate of change of power Left on 100 days in a satellite. If the power supply in the satellite this P. L. Is equal to 100 ft times each of the negative zero point 0052. Which is a number of age. Now we have to find the rate of change of power. Then we could differentiate the given power respect to time. So DP DT that is equal to negative zero coins. But time speed to the -0.0052. Now the time rate of change of power 108. We did calculate that by substitution and see Let's see if he puts 100 into the derivative of chain right here. And then we get DP DT that's equal to negative zero point 303. And that's the rate of change of power after 100 days.

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