OCR MEI C3 2007 June — Question 4

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2007
SessionJune
TopicExponential Functions

4 A cup of water is cooling. Its initial temperature is \(100 ^ { \circ } \mathrm { C }\). After 3 minutes, its temperature is \(80 ^ { \circ } \mathrm { C }\).
  1. Given that \(T = 25 + a \mathrm { e } ^ { - k t }\), where \(T\) is the temperature in \({ } ^ { \circ } \mathrm { C } , t\) is the time in minutes and \(a\) and \(k\) are constants, find the values of \(a\) and \(k\).
  2. What is the temperature of the water
    (A) after 5 minutes,
    (B) in the long term?