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Solve the given problems by finding the appropriate derivative.A metal bar is heated, and then allowed to cool. Its temperature $T$ $\left(\text { in }^{\circ} \mathrm{C}\right)$ is found to be $T=15+75 e^{-0.25 t},$ where $t$ (in min) is the time of cooling. Find the time rate of change of temperature after 5.0 min.

$-5.4^{\circ} \mathrm{C} / \mathrm{min}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

Derivatives

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We need to find the time rate of change of temple for me to embark after five minutes. If the temperature is expressed by T And it's equal to 13. Look, count to five. Mhm. To the zero 0.25 T. So the time rate of change of temperature can be obtained by different change given equation of our temperature. So the team T. C. That's equal through- 18.75. Some speech and negative. They're .25. Now we can find a time really change of temperature after five minutes but 50 tune and C. Is equal to five. Enter the equation and that gives you -5.4 and that's the time we will change the temperature. The negative sign indicates that the temperature decreases with time.

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