A turkey is removed from the oven when its temperature reaches $185^\circ F$ and is placed on a table in a room where the temperature is $75^\circ F$. After $10$ minutes, the temperature of the turkey is $172^\circ F$, and after $20$ minutes, it is $160^\circ F$. Use a linear approximation to predict the temperature of the turkey after half an hour (use secant slopes as an approximation for the derivative).

$^\circ F$