A ceramic component is removed from a firing oven at a 1000 K, and left to cool in a temperature controlled environment of 295 K.

The component cools according to the relationship shown in the following equation:

\normalsize\frac{dT}{dt} = k (T - T_a) 

where T is the temperature of the component, t is time, k is a constant with value of -0.0185, and T_a is the temperature of the temperature controlled environment.

What is the error between the analytical solution and a 50 step Euler method at 60 minutes?