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2. For times t > 0, a certain temperature is given by the function T(t) = = where t is in minutes and T is in °C. 10t² e €0.3t Before answering the questions below, use a graphing utility (desmos.com is good) to graph this temperature function for t≥ 0. Think about how the graph of dT/dt should look. Display the graphs of T(t) and dT/dt together and see how accurate your thoughts were. a) Use calculus and hand-calculations to find an exact expression for the maximum temperature that is reached (your answer will involve e).

2. For times t > 0, a certain temperature is given by the function T(t) = = where t is in minutes and T is in °C. 10t² e €0.3t Before answering the questions below, use a graphing utility (desmos.com is good) to graph this temperature function for t≥ 0. Think about how the graph of dT/dt should look. Display the graphs of T(t) and dT/dt together and see how accurate your thoughts were. a) Use calculus and hand-calculations to find an exact expression for the maximum temperature that is reached (your answer will involve e).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. For times t > 0, a certain temperature is given by the function T(t) = €0.3t 10t² where t is in minutes and T is in °C. e Before answering the questions below, use a graphing utility (desmos.com is good) to graph this temperature function for t≥ 0. Think about how the graph of dT/dt should look. Display the graphs of T(t) and dT/dt together and see how accurate your thoughts were. a) Use calculus and hand-calculations to find an exact expression for the maximum temperature that is reached (your answer will involve e).
Transcribed Image Text:2. For times t > 0, a certain temperature is given by the function T(t) = €0.3t 10t² where t is in minutes and T is in °C. e Before answering the questions below, use a graphing utility (desmos.com is good) to graph this temperature function for t≥ 0. Think about how the graph of dT/dt should look. Display the graphs of T(t) and dT/dt together and see how accurate your thoughts were. a) Use calculus and hand-calculations to find an exact expression for the maximum temperature that is reached (your answer will involve e).
Expert Solution
Step 1

Here the graph in the red line is the graph of the function, where the graph in the blue line is graph of the derivative of the function. As shown in the calculation we can easily see that graphical data matches with the hand calculations.

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