Edexcel IALMathematicsGeneral Applications12 Marks
The amount of a drug in a patient's bloodstream, D mg, t hours after the drug has been administered, is modelled by the differential equation dD/dt = 1/20 D(4-D). Given that D=1 when t=0.
- (a)Show that ∫ 1/(D(4-D)) dD = 1/4 ∫ ( 1/D + 1/(4-D) ) dD.[3]
- (b)Hence find an expression for D in terms of t.[9]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) M1: for attempting to split 1/(D(4-D)) into partial fractions.
- (a) A1: for correct partial fractions.
- (a) A1: for showing the required result.
- (b) M1: for separating variables.
- (b) M1: for integrating LHS to involving ln terms.
- (b) M1: for integrating RHS to 1/20t (+c).
- (b) A1: for correct integration.
- (b) M1: for using D=1, t=0 to find c.
- (b) A1: for correct c.
- (b) M1: for using log rules to combine ln terms.
- (b) M1: for converting to exponential form.
- (b) A1: for correct expression for D.
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