| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Exponential Functions |
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9. A cup of tea is cooling down in a room.
The temperature of tea, \(\theta ^ { \circ } \mathrm { C }\), at time \(t\) minutes after the tea is made, is modelled by the equation
$$\theta = A + 70 e ^ { - 0.025 t }$$
where \(A\) is a positive constant.
Given that the initial temperature of the tea is \(85 ^ { \circ } \mathrm { C }\)
a. find the value of \(A\).
b. Find the temperature of the tea 20 minutes after it is made.
c. Find how long it will take the tea to cool down to \(43 ^ { \circ } \mathrm { C }\).
(4)