While using python:

3. The rate of cooling of a body can be expressed as dT -K(T-T) dt where T = temperature of the body (C) Ta= temperature of the surrounding medium (C) k = proportionality constant (per minute) This equation is called Newton's law of cooling. 20C. Now, imagine that a metal ball heated to 80C is dropped into water that is held constant at Ta The temperature T of the ball changes with time as shown in the table below. 0 5 10 15 20 25 Time t (min) T (C) 80 44.5 30.0 24.1 21.7 20.7 a. Use a first-order backward-differenced Taylor series expansion to calculate an array of dT /dt values alongside the values of time t, up to 25 min. b. Calculate and print the average value of k that you can find from the arrays of dT /dt and T values. 3. The rate of cooling of a body can be expressed as dT -K(T-T) dt where T = temperature of the body (C) Ta= temperature of the surrounding medium (C) k = proportionality constant (per minute) This equation is called Newton's law of cooling. 20C. Now, imagine that a metal ball heated to 80C is dropped into water that is held constant at Ta The temperature T of the ball changes with time as shown in the table below. 0 5 10 15 20 25 Time t (min) T (C) 80 44.5 30.0 24.1 21.7 20.7 a. Use a first-order backward-differenced Taylor series expansion to calculate an array of dT /dt values alongside the values of time t, up to 25 min. b. Calculate and print the average value of k that you can find from the arrays of dT /dt and T values