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]
