Suppose the temperature of a cup of tea in degrees Fahrenheit minutes after it has been poured may be modeled by the equation .
a) What is the temperature of the tea after 3 hours?
degrees Fahrenheit
b) How long does it take for the cup of tea to cool to 100 degrees?
minutes
c) What does each part of this equation mean?
A:
B:
C:
a) You need to evaluate the function at 3 hours. Note that the input units are in minutes, so you will need to convert 3 hours to minutes before evaluating the function.
b) We want to find the time in minutes at which the temperature of the tea is 100 degrees Fahrenheit. This can be done by setting the model equal to 100 and solving for . That is, we want to solve
for .
Note that you will need to use logarithms to do this.
c) Try to use process of elimination to answer these interpretations. It may be easiest to identify the initial value or growth factor first.
You can also think about what happens to the function after a long amount of time. In context, does it make sense to have a sort of cut-off value for the temperature? What would that temperature represent?