OCR C4 2007 June — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2007
SessionJune
TopicDifferential equations

8 The height, \(h\) metres, of a shrub \(t\) years after planting is given by the differential equation $$\frac { \mathrm { d } h } { \mathrm {~d} t } = \frac { 6 - h } { 20 }$$ A shrub is planted when its height is 1 m .
  1. Show by integration that \(t = 20 \ln \left( \frac { 5 } { 6 - h } \right)\).
  2. How long after planting will the shrub reach a height of 2 m ?
  3. Find the height of the shrub 10 years after planting.
  4. State the maximum possible height of the shrub.