Suppose the temperature of a cup of tea in degrees Fahrenheit $t$ minutes after it has been poured may be modeled by the equation $T(t)=111 (0.92)^{t}+79$.

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?

$T(t)=\underbrace{111}_{A} (\underbrace{0.92}_{B})^{t}+\underbrace{79}_{C}$

A: ? This represents the temperature of the room the cup is in This represents the rate at which the tea is decreasing in temperature every minute This represents the how much hotter than room temperature the initial temperature of the tea is

B: ? This represents the temperature of the room the cup is in This represents the rate at which the tea is decreasing in temperature every minute This represents the how much hotter than room temperature the initial temperature of the tea is

C: ? This represents the temperature of the room the cup is in This represents the rate at which the tea is decreasing in temperature every minute This represents the how much hotter than room temperature the initial temperature of the tea is

Hint: