Julie has a fresh cup of hot coffee that has a temperature of $180^\circ \text{F}$. The temperature of the room is $70^\circ$. Let $t =$ number of minutes after Julie poured her coffee, and let $d =$ the number of degrees the coffee is warmer than room temperature. In this situation $d = km^{t}$ for some constants $k$ and $m$.

1. Five minutes after Julie pours her coffee, its temperature is down to $160^{\circ}\text{F}$. Find $k$ and $m$, and then write the particular equation for this situation.

   Hint 1(a):

   Remember that $d =$ degrees above $70^\circ$.
   1. Use the given information to write the coordinates of two points. Substitute them into the given situation for '$d$' and '$t$'.
   2. Then you will have two equations and two unknowns.
   3. Solve for the unknowns.

   Hint 2(a):

   Divide one of the equations by the other in other to solve!

   Answer (a):

   $d = 110\left(5\sqrt{\frac{9}{11}}\right)^t$

2. What does your model (equation) predict for the temperature of the coffee $10$ minutes later ($15$ minutes after it was poured)?

   Answer (b):

   $130.248 ^\circ \text{F}$
   Did you remember to add $70^\circ$ to the answer using the above equation?