## Exam Style Question on Exponential Models## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 136. This question is similar to one that appeared in a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

The quantity of heat required to heat an amount of water is given by the formula:

$$H = atI^2 – b$$Where \(H\) is the number of calories delivered by an electric current of \(I\) amps acting for \(t\) seconds and \(a\) and \(b\) are constants.

(a) Rearrange the formula to make \(I\) the subject.

The graph below gives information about the cooling of a cup of coffee on a cold day. The vertical axes shows the variation in the temperature, \(T\), and the horizontal axis shows the time, \(t\), in seconds.

(b) Work out the average rate of decrease of the temperature of the coffee between \(t = 0\) and \(t = 700\).

The instantaneous rate of decrease of the temperature of the water at time \(A\) seconds is equal to the average rate of decrease of the temperature of the water between \(t = 0\) and \(t = 700\).

(c) Find an estimate for the value of \(A\) showing how you got your answer.

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