### Home > CALC > Chapter 7 > Lesson 7.3.4 > Problem 7-148

7-148.

Let

*y*(*t*) denote the temperature (in °F) of a cup of tea at time*t*(in minutes). The temperature of the tea starts at 190°, while the room temperature is 70°. The tea's change in temperature is described by the equation: Homework Help ✎= −0.1( *y*− 70)Describe the change in temperature of the tea in relation to the room temperature.

How hot is the tea at any time

*t*?How hot is the tea after 10 minutes?

As time goes on, will the tea ever become colder than the room temperature?

Implicitly integrate to find *y*(*t*).

Find the value of '*C*' by evaluating the initial condition: when *t* = 0, *y* = 190.

*y* = 70 + 120*e*^{−0.1}^{t}

*y*(10) = ________________