Separable Differential Equations

Question

A thermometer is taken from a room where the temperature is 23 degrees C to the outdoors, where the temperature is −11 degrees C. After one minute the thermometer reads 14 degrees C. 

(a) What will the reading on the thermometer be after 2 more minutes? 

(b) When will the thermometer read -10 degrees C?

Answer 1

Assuming Newton's law of cooling: dT/dt = -h(T-T_∞) T = T₀ - (T₀ - T_∞) e^-ht

a) solve for h given t, T₀, T_∞, and T(t). Then solve for T(3 min)

b) solve for t given T = -11°