2017 AP Calculus AB/BC 4c | AP Calculus AB solved exams | AP Calculus AB | Khan Academy | Summary and Q&A
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TL;DR
This video explains how to solve a separable differential equation to find the internal temperature of a potato at a specific time.
Key Insights
- 🏛️ The problem in the video is likely from an AP calculus class, as it involves solving a differential equation.
- ❓ A separable differential equation can be solved by separating the variables and integrating each side.
- ❓ The initial condition, or a known value of the function, can be used to find the constant value in the general solution.
- ⌛ The specific temperature at a given time can be found by substituting the time value into the expression for the function.
- 🦖 The internal temperature of the potato is found to be 54 degrees Celsius at time T = 3.
- 😑 Algebraic manipulation is necessary to solve the differential equation and find the final expression for G(T).
Transcript
- [Instructor] Let's now tackle part C which tells us, for T is less than 10, an alternate model for the internal temperature of the potato at time T minutes is the function G that satisfies the differential equation. The derivative of G with respect to T is equal to the negative of G minus 27 to the two third power. Where G of T is measured in deg... Read More
Questions & Answers
Q: What kind of differential equation is being solved in this video?
This video solves a separable differential equation, which means the variables can be separated on different sides of the equation before integrating.
Q: How is the initial condition used to find the constant value in the expression for the internal temperature?
The initial condition, G(0) = 91, is substituted into the expression and solved for the constant value. In this case, C is found to be equal to 12.
Q: How is the internal temperature of the potato determined at a specific time?
By substituting the time value into the expression for G(T), the video demonstrates how to find the internal temperature of the potato at that time.
Q: What units are used for the internal temperature in this problem?
The internal temperature of the potato is measured in degrees Celsius.
Summary & Key Takeaways
-
The video teaches how to solve a separable differential equation to find an expression for the internal temperature of a potato.
-
The initial condition given in the problem is used to find the constant value in the expression for the internal temperature.
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By substituting the time value into the expression, the video demonstrates how to determine the internal temperature of the potato at that specific time.
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