Refrigeration was essential to preserve the soup overnight. However, the soup was too hot to be put directly into the fridge when it was ready (at 100 degress celsius), and the fridge was not powerful enough to preserve the soup if it was warmer than 20 degrees celsius. He cooled the pot in a sink full of cold running water, which produced a constant temperture of 5 degrees celsius, and stirred occasionally. By doing this, he could bring the temperature of the soup up to 60 degress celsius in 10 mins.
a. Given the model T(t)=Ts+(T0-Ts)e^(-kt) and that T(t) = temperature at given time, t, Ts= temperature of surroundings, T0=inital temperature, and k=constant, find the exact value of k.
b. Write a function that models this situation
c. How long before closing time should the soup be ready so that Jim could put it in the fridge and leave on time?