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Exam-Style Question on Exponential Models

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

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Question id: 209. This question is similar to one that appeared on an IB Studies paper in 2015. The use of a calculator is allowed.

A cup of hot tea is placed on a table to cool. The temperature of the room is 24oC.

This situation can be modelled by the exponential function:

$$T = a + b (k^{-m})$$

where \(T\) is the temperature of the water, in oC, and \(m\) is the number of minutes for which the cup has been placed on the table.


(a) Find the value of \(a\)

Initially the temperature of the tea is 92oC.

(b) Find the value of b.

After one minute, the temperature of the tea is 74oC.

(c) Find the value of \(k\).

(d) Find the temperature of the tea three minutes after it has been placed on the table.

(e) Find the total time needed for the tea to reach a temperature ofof 30oC. Give your answer in minutes and seconds, correct to the nearest second.

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