In the court case Liebeck v. McDonald’s (1994), a woman sued McDonald’s restaurant for serving coffee at a temperature of 180° that caused her to be severely burned when the coffee spilled. An expert witness at the trial testified that liquids at 180° will cause a full thickness burn to human skin in two to seven seconds. It was stated that had the coffee been served at 155°, the liquid would have cooled and avoided the serious burns. The woman was awarded over 2.7 million dollars. Because of this famous case, many restaurants now serve coffee at a temperature around 155°. The function below models the temperature of the coffee:

T(m) =108e-0.018m+72

a) Algebraically determine how long, to the nearest hundredth of a minute, would McDonald’s need to wait in order to serve the coffee at 155°?

b) Interpret what each of the numbers in the function represent.

c) Over time, what temperature would coffee approach?