OCR C3 2012 January — Question 7

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2012
SessionJanuary
TopicExponential Functions

7
  1. Substance \(A\) is decaying exponentially and its mass is recorded at regular intervals. At time \(t\) years, the mass, \(M\) grams, of substance \(A\) is given by $$M = 40 \mathrm { e } ^ { - 0.132 t }$$ (a) Find the time taken for the mass of substance \(A\) to decrease to \(25 \%\) of its value when \(t = 0\).
    (b) Find the rate at which the mass of substance \(A\) is decreasing when \(t = 5\).
  2. Substance \(B\) is also decaying exponentially. Initially its mass was 40 grams and, two years later, its mass is 31.4 grams. Find the mass of substance \(B\) after a further year.