2017 AP Calculus AB/BC 4c | AP Calculus AB solved exams | AP Calculus AB | Khan Academy

TL;DR

This video explains how to solve a separable differential equation to find the internal temperature of a potato at a specific time.

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

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).

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.

• By substituting the time value into the expression, the video demonstrates how to determine the internal temperature of the potato at that specific time.