Let $y(t)$ denote the temperature (in $^\circ\text{F}$) of a cup of tea at time $t$ (in minutes). The temperature of the tea starts at $190^\circ$, while the room temperature is $70^\circ$. The tea’s change in temperature is described by the equation:

$\frac { d y } { d x }= −0.1(y − 70)$

1. ​Describe the change in temperature of the tea in relation to the room temperature.

   Hint (a):

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

2. What is the temperature of the tea at any time $t$?

   Step 1(b):

   Implicitly integrate to find $y\left(t\right)$.

   Step 2(b):

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

   Answer (b):

   $y = 70 + 120e^{−0.1t}$

3. What is the temperature of the tea after $10$ minutes?

   Hint (c):

   $y\left(10\right) =$ ________________