A hot drink is taken outside on a cold winter day when the air temperature is −5°C. According to a principle of physics called Newton’s law of cooling, the temperature T (in degrees Celsius) of the drink t minutes after being taken outside is given by a function of the form

where A and k are constants. Suppose the temperature of the drink is 80°C when it is taken outside and 20 minutes later is 25°C.

a. Use this information to determine A and k.

b. Sketch the graph of the temperature function T(t). What happens to the temperature as t increases indefinitely (t → + ∞?

c. What will the temperature be after 30 minutes?

d. When will the temperature reach 0°C?

Transcribed Image Text:

T(t) = −5+ Ae¯kt