The temperature TTT °C of a drink, t t\,t minutes after it is poured, is modelled by
T=20+80e−0.2tT=20+80e^{-0.2t}T=20+80e−0.2t.
Show that the time at which T=35T=35T=35 satisfies
20+80e−0.2t−35=020+80e^{-0.2t}-35=020+80e−0.2t−35=0.
Starting with t0=8t_0=8t0=8, use Newton–Raphson iteration to find t1t_1t1, t2 t_2\,t2 and t3t_3t3. Give each value to six decimal places.
State the time, to the nearest second, at which the model predicts that the drink reaches 35 °C.
125 exam-style questions on CCEA A Level Maths 3.7 Numerical methods (A-level only), covering 3.7.1 Numerical methods (A-level only), 3.7.2 Numerical methods (A-level only), 3.7.3 Numerical methods (A-level only), and 3.7.4 Numerical methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.