A hot metal bar is submerged in a large reservoir of water whose temperature is 45 F . The rate of change of the temperature of the metal bar is proportional to the difference between the temperature of the bar and the temperature of the reservoir. (Since the bar is cooling off, write the proportionality constant as -k instead of k.) The temperature of the bar 20s after submersion is 85 F. After 1 minute submerged, the temperature has cooled to 65 F. To answer the following questions, you will need to write the differential equation describing this scenario. Determine the cooling constant k.

Question

A hot metal bar is submerged in a large reservoir of water whose temperature is 45 F . The rate of change of the temperature of the metal bar is proportional to the difference between the temperature of the bar and the temperature of the reservoir. (Since the bar is cooling off, write the proportionality constant as -k instead of k.) The temperature of the bar 20s after submersion is 85 F. After  1 minute submerged, the temperature has cooled to 65 F. To answer the following questions, you will need to write the differential equation describing this scenario. Determine the cooling constant k.