A cup of coffee is made with boiling water (100 degreeC) and stands in a room wh

Question

A cup of coffee is made with boiling water (100 degreeC) and stands in a room where the temperature is a constant 21 degreeC. If T(t) is the temperature of the coffee at time t (measured in minutes), what does the differential equation below mean? dt/dt = -k(T - 21) The rate at which the temperature changes is proportional to the temperature of the coffee. The rate at which the temperature changes is proportional to the difference between the temperature of the coffee and that of the room. The rate at which the temperature changes is proportional to the temperature of the coffee and that of the room. The rate at which the temperature changes is proportional to the temperature of the room. What is the sign of k? positive zero negative Solve this differential equation. Your answer will have k in it. Use lower case k. T(t) = If the coffee cools to 90 degreeC in 3 minutes, find k. Round your answer to 4 decimal places. How long will it take for the coffee to cool to 60 degreeC? Round your answer to one decimal place. minutes

Explanation / Answer

) The rate at which temperature changes is proportinal to the difference between temp. of coffee and that room

b)positive

c)21+79*e^(-kt)

d)0.0451

e)15.7

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