# 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: 136. This question is similar to one that appeared on 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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