- Coffee is poured into a cup.
The temperature of the coffee, \(H ^ { \circ } \mathrm { C } , t\) minutes after being poured into the cup is modelled by the equation
$$H = A \mathrm { e } ^ { - B t } + 30$$
where \(A\) and \(B\) are constants.
Initially, the temperature of the coffee was \(85 ^ { \circ } \mathrm { C }\).
- State the value of \(A\).
Initially, the coffee was cooling at a rate of \(7.5 ^ { \circ } \mathrm { C }\) per minute.
- Find a complete equation linking \(H\) and \(t\), giving the value of \(B\) to 3 decimal places.