Final answer:
The differential equation that fits the physical description is dT/dt = k(M - T).
Step-by-step explanation:
The given physical description can be represented by a differential equation. Let's denote the temperature of the coffee at time t as T(t), and the temperature of the air at time t as M(t). According to the description, the rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t. Mathematically, this can be written as:
dT/dt = k(M - T)
Where k is the proportionality constant. Here the details:
- The rate of change in the temperature of coffee (dT/dt) represents the derivative of the temperature with respect to time.
- The difference between the temperature of the air (M) and the temperature of the coffee (T) represents the driving force for the temperature change.
- The proportionality constant (k) determines how fast the temperature of the coffee changes in response to the temperature difference.
The complete question:
- Write a differential equation that fits the physical description. The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t.