You plan on cooking a lamb roast for some fellow students.  You take it from the bench  (where the lamb was at a room temperature of 20 degrees) and place it in an oven that is at a constant temperature of 180 degrees celsius.  After 10 minutes you check the temperature of the lamb using a meat thermometer and it has increased to 28 degrees celsius. Your fellow students are fussy and have requested that you produce a perfect medium rare roast with an internal temperature of 55 degrees. You know that Newton's law of cooling can also be applied to situations where we are heating something, so plan on applying the law to this situation.  This will produce an ODE which can be solved and will give an answer involving a steady state and transient component of the form 𝑇 = 180 − 𝐴 𝑒 − 𝑘 𝑡 where t is measured in minutes and T is measured in degrees celsius.  One of your fellow students has said that if you find the values of A and k for them they are confident they can use your model to determine exactly how long you should cook the roast for. Create an ODE that models the situation (including writing down the initial condition) and solve this ODE to find a formula for T  of the form given above. What is the value of k?  Enter your answer to 4 decimal places, rounding as appropriate.  Note that k will be a positive value (as the negative sign is placed in front of k).简答题