Potato Temperature Change Analysis

The video tutorial covers the 2017 AP Calculus exam's potato cooling problem. It explains how the internal temperature of a potato, initially at 91°C, cools over time in a room with an ambient temperature of 27°C. The cooling process is modeled by a differential equation. The tutorial derives the equation for the tangent line at T=0 and uses it to approximate the potato's temperature at T=3.

What is the initial internal temperature of the potato at time T equals zero?

• 27 degrees Celsius

• 50 degrees Celsius

• 91 degrees Celsius

• 100 degrees Celsius

What is the ambient room temperature assumed to be in the problem?

• 30 degrees Celsius

• 25 degrees Celsius

• 27 degrees Celsius

• 20 degrees Celsius

What does the differential equation describe in the context of the potato problem?

• The rate of heating of the potato

• The constant temperature of the potato

• The increase in ambient temperature

• The rate of cooling of the potato

How does the rate of change of temperature relate to the difference between the potato's temperature and the ambient temperature?

• It is directly proportional

• It is unrelated

• It is constant

• It is inversely proportional

What shape does the graph of the potato's temperature over time resemble?

• A straight line

• A parabola

• An exponential decay curve

• A sine wave

What happens to the rate of change as the potato's temperature approaches the ambient temperature?

• It remains constant

• It becomes more positive

• It becomes less negative

• It becomes zero

What is the equation of the tangent line to the graph of H at T equals 0?

• Y = -16T + 91

• Y = 1/4T + 27

• Y = 16T + 91

• Y = -1/4T + 27

How is the tangent line used to approximate the temperature at T equals 3?

• By using the original differential equation

• By measuring the actual temperature

• By finding the slope at T equals 3

• By evaluating the tangent line equation at T equals 3

What is the approximate internal temperature of the potato at T equals 3 using the tangent line?

• 27 degrees Celsius

• 43 degrees Celsius

• 91 degrees Celsius

• 64 degrees Celsius

Why is the rate of change of temperature negative in this problem?

• Because the ambient temperature is increasing

• Because the potato is heating up

• Because the ambient temperature is decreasing

• Because the potato is cooling down