OCR C3 Specimen — Question 5

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
SessionSpecimen
TopicDifferentiating Transcendental Functions

5 At time \(t\) minutes after an oven is switched on, its temperature \(\theta ^ { \circ } \mathrm { C }\) is given by $$\theta = 200 - 180 \mathrm { e } ^ { - 0.1 t }$$
  1. State the value which the oven's temperature approaches after a long time.
  2. Find the time taken for the oven's temperature to reach \(150 ^ { \circ } \mathrm { C }\).
  3. Find the rate at which the temperature is increasing at the instant when the temperature reaches \(150 ^ { \circ } \mathrm { C }\).