Exam-Style Question on Exponential Models

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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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