A student builds a simple circuit with a single resistor of resistance 2R2R2, R and current III, and measures an electric potential difference of \Delta V_1ΔV 1 delta, V, start subscript, 1, end subscript across the resistor. Then, the student decreases the current through the circuit to \dfrac{I}{2} 2 I start fraction, I, divided by, 2, end fraction.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.