Exam-Style Question on Iteration

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 619. This question is similar to one that appeared on a GCSE Higher paper in 2020. The use of a calculator is allowed.

A large mug of hot tea is cooling on a small lounge table.

The temperature $$n$$ minutes after 2pm is $$T_n$$ degrees Celsius.

The temperature of the tea (n+1) minutes after 2pm, $$T_{n + 1}$$ metres, is given by:

$$T_{n + 1} = A × T_n + 24$$

where $$A$$ is a constant.

At 2pm the tea is a piping hot 84°.

At 14:01 temperature of the tea is 80°.

Work out the temperature of the tea at 14:03

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