Edexcel IALMathematicsGeneral Applications3 Marks
The value, V, of a product, t years after it was launched, is modelled by the differential equation dV/dt = kV/(t + 1), where k is a constant. Given that the value of the product halves in the first year, (b) find the value of k, giving your answer to 3 significant figures.
- (b)find the value of k, giving your answer to 3 significant figures.[3]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for setting up the equation using the given information: V = V₀/2 when t = 1. So, V₀/2 = V₀(1 + 1)^k.
- A1 for correctly solving for k: 1/2 = 2^k => k = -1.
- A1 for k = -1.00 (to 3 s.f. or more accurately as exact value is -1).
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