📐 Formula Modeling Easy

Coffee Cooling Model

Problem Description

A cup of coffee is placed in a room with constant ambient temperature. Temperature measurements are recorded every minute for 60 minutes.

Your task:

  1. Identify the appropriate mathematical model that describes the cooling process
  2. Write the differential equation governing the system
  3. Provide the analytical solution
  4. Estimate the model parameters from the data

Observed Data

60 measurements, 1 per minute

Scoring Rubric

Your Submission

Write the ODE governing the cooling process in LaTeX

LaTeX preview

Write the solution T(t) in LaTeX

LaTeX preview
min⁻¹
°C
°C

Evaluation Result

AI-powered assessment based on rubric

/100

Overall Assessment

💡 Improvement Suggestions

📌 Reference Answer

Differential Equation (Newton's Law of Cooling)

Analytical Solution

k

0.032

min⁻¹

T₀

90.0

°C

T_env

25.0

°C