1. You buy a coffee in Tim Hortons, where the ambient temperature is 25 C, and measure its temperature to be 70 C using a thermometer. After 5 minutes of using the free Tim Hortons WiFi, and neglecting to drink your coffee, you find that it is now at 60 C. You then head outside, put your coffee down on a picnic table to tie your shoe, and walk to class. 15 minutes after buying the coffee, you arrive at your lecture hall and realize that you left the still completely full coffee back at the Tim Hortons picnic table. After walking all the way back to the Tim Hortons, you finally take your first sip of coffee. What temperature is the coffee at this point in time? (a) (4 pts) Assuming a fixed outdoor temperature of 15C. (b) (2 pts) Assuming a variable outdoor temperature, given by 13.C + 2Ccos (27 t) where t is the time in minutes since you started walking to class. Hint: In order to solve this problem, you will need to use Newton's law of cooling, to write down an ODE of the form y' + ay = b with constants a and b. The value of a can be determined by solving the ODE and matching the solution to data from the problem statement