Math Problem Statement
When coffee is poured into a mug with no lid, its temperature is measured at 170◦F. Three minutes later its temperature is 165◦F. Also, the surrounding temperature at the coffee shop is set to 68◦F. a. Write an initial value problem that will describe the change in the temperature of the coffee, T , as a function of time t measured in minutes
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Newton's Law of Cooling
Formulas
dT/dt = -k (T(t) - T_ambient)
T(t) = T_ambient + (T(0) - T_ambient) * e^(-kt)
Theorems
Newton's Law of Cooling
Suitable Grade Level
Grades 11-12
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