- A quantity of ethanol was heated until it reached boiling point.
The temperature of the ethanol, \(\theta ^ { \circ } \mathrm { C }\), at time \(t\) seconds after heating began, is modelled by the equation
$$\theta = A - B \mathrm { e } ^ { - 0.07 t }$$
where \(A\) and \(B\) are positive constants.
Given that
- the initial temperature of the ethanol was \(18 ^ { \circ } \mathrm { C }\)
- after 10 seconds the temperature of the ethanol was \(44 ^ { \circ } \mathrm { C }\)
- find a complete equation for the model, giving the values of \(A\) and \(B\) to 3 significant figures.
Ethanol has a boiling point of approximately \(78 ^ { \circ } \mathrm { C }\)
Use this information to evaluate the model.