4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), dtdT= k(TTa), where T is the temperature of the body, t is time, k is the proportionality constant, and Ta is the ambient temperature. (1) Suppose that a cup of coffee originally had a temperature of 70C. Use Euler's method to compute the temperature from t=0 to 10min using a step size of 2min if Ta=20C and k=0.02/min. Present your calculations carefully. (2) Compare your results in (1) with an analytical solution. List your results in a table containing four columns: time, numerical results, analytical results, true percentage error (\%) with four significant figures. Is your numerical solution higher or lower than the analytical solution? Why? (3) One student employed Euler's method to solve this problem and reported that the temperature was 68C after two steps. Compare this value with your results in (1) and comment whether he used a larger or smaller timestep than (1). What is the timestep that was used here