Math Problem Statement
Suppose that a cup of coffee begins at 172◦ F and after sitting in room temperature of 66◦ F for 14 minutes, the coffee reaches 165◦ F.
The differential equation is T(t) = 106e^(1/14ln(99/106)t+66
How long will it take before the coffee reaches 154 degrees? Include at least 2 decimal places in your answer.
? minutes
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Decay
Logarithmic Functions
Differential Equations
Newton's Law of Cooling
Formulas
T(t) = 106e^(1/14 * ln(99/106) * t) + 66
t = ln(88/106) / (1/14 * ln(99/106))
Theorems
Newton's Law of Cooling
Suitable Grade Level
Grades 11-12
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