OCR MEI C3 2012 January — Question 6

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2012
SessionJanuary
TopicNon-constant acceleration

6 Oil is leaking into the sea from a pipeline, creating a circular oil slick. The radius \(r\) metres of the oil slick \(t\) hours after the start of the leak is modelled by the equation $$r = 20 \left( 1 - \mathrm { e } ^ { - 0.2 t } \right) .$$
  1. Find the radius of the slick when \(t = 2\), and the rate at which the radius is increasing at this time.
  2. Find the rate at which the area of the slick is increasing when \(t = 2\).