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Warming up a Solar Cell

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The temperature T˚C of a solar cell during a 24 hour period is modelled as 

\[T = 20 – k\left( 15 – \frac{5t}{4} \right)^{2}\ ,\ \ \ 0 \leq t \leq 24\]

Where t is the time in hours after midnight and k is a positive constant

The temperature of the solar cell at midnight is 5˚C.

a) Use this information to find the value of k in the model.

[2 marks]

b) Find, according to the model, the temperature of the solar cell at 8:30 am.

[2 mark]

c) Determine the greatest temperature of the solar cell and the time at which this temperature occurs.

[3 marks]

d) State one limitation of the model

[1 mark]

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