Differential Equations - Newton's law of cooling

Question

A hot cup of coffee at 90°C is placed on a table in the kitchen where the room temperature is 20°C. Using Newton's law of cooling, find at what rate the temperature of the coffee was decreasing when it was placed on the table. Give correct units.

Additional information: After 10 minutes the temperature of the coffee was 60°C.

Answer 1

T(t) = T_s + (T_o – T_s) e^-kt_; T(10) = 60 = 20 + (90 - 20)e^-10k; 40 = 70e^-10k; k = - 0.1ln(4/7) = 0.056 min^-1