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3.7 Numerical methods (A-level only)

3.7 Numerical methods (A-level only)

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Question 4

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.

a.

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.

[1]
b.

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.

[5]
c.

State the time, to the nearest second, at which the model predicts that the drink reaches 35 °C.

[2]
Markscheme

3.7 Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Numerical methods (A-level only)

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.

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