Starbucks serves coffee at 170◦ and the room temperature in Starbucks is 70◦. The coffee cools to 100◦ after 10 minutes. Let T(t) be the temperature of the coffee at timet, measured in minutes.

(a) Write down the differential equation for T (t) and determine a formula for T (t).

(b) From the time when the temperature is 100◦ at t = 10, how many additional minutes will it take for the temperature of the coffee to reach 80◦? Round your answer to one digit after the decimal point.