Edexcel IALMathematicsGeneral Applications9 Marks
The value of a car, V, in pounds, can be modelled by the equation V = Ae^(-kt), where t is the age of the car in years, and A and k are positive constants. When the car is new, its value is £20 000. When the car is 5 years old, its value is £12 000.
- (a)Find the value of A and show that k = 1/5 ln(5/3).[3]
- (b)Find the age of the car when its value is £5000. Give your answer to one decimal place.[2]
- (c)(i)Find dV/dt in terms of A, k and t.[2]
- (c)(ii)Hence find the rate at which the value of the car is decreasing when t=10. Give your answer to the nearest pound per year.[2]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) M1: for using t=0, V=20000 to find A.
- (a) M1: for using t=5, V=12000 and A=20000 to set up an equation in k.
- (a) A1: for showing k = 1/5 ln(5/3).
- (b) M1: for setting V=5000 and solving for t.
- (b) A1: for correct t.
- (c)(i) M1: for differentiating V with respect to t.
- (c)(i) A1: for correct derivative.
- (c)(ii) M1: for substituting t=10 and their A and k into their dV/dt.
- (c)(ii) A1: for correct rate of decrease.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →