The amount of a drug, D mg, in a patient's bloodstream t hours after it has been administered, is given by the formula D = 10e^(-0.2t).

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. (a) B1 for substituting t=0 into D = 10e^(-0.2t) to get D = 10 (mg)
2. (b) M1 for setting D = 2: 2 = 10e^(-0.2t)
3. (b) A1 for e^(-0.2t) = 0.2 (o.e. as 1/5)
4. (b) M1 for taking natural logarithms: -0.2t = ln(0.2)
5. (b) A1 for t = -ln(0.2) / 0.2 = 8.05 hours (3 s.f.) (accept 8.047... rounded to 3 s.f.)
6. (c) M1 for differentiating D with respect to t: dD/dt = 10(-0.2)e^(-0.2t) or Akekt form
7. (c) A1 for dD/dt = -2e^(-0.2t)
8. (c) A1 for substituting t=5: dD/dt = -2e^(-0.2*5) = -2e^(-1) = -0.736 mg/hour (3 s.f.) (allow 0.736 as the rate of decrease)