Higher November 2019 Paper 1 Q17
17.
(a) \[\begin{aligned} V_0 &= 10\,000 \\ V_{n+1} &= 0.8\,V_n \quad \text{where} \quad n \geqslant 0 \end{aligned}\]This iterative formula can be used to work out the value \(V_n\) of a particular type of car when it is \(n\) years old.
(i) Show that a car of this type that is 1 year old is worth £8000. [1]
(ii) Use this formula to find the value of a car of this type that is 3 years old. [3]
(b) A newly built house is worth £240 000 and is expected to increase in value by 2% each year.
Complete the following iterative formula to show this information. [1]
Complete the following iterative formula to show this information. [1]
\(V_0 =\) ..............................
\(V_{n+1} =\) .................... \(V_n \quad \text{where} \quad n \geqslant 0\)
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(V_1 = 0.8 \times 10000\) ( = 8000) | B1 | |
| (ii) \(V_2 = 0.8 \times V_1 = 6400\) si | B1 | Allow poor use of notation |
| \(V_3 = 0.8 \times V_2 = 0.8 \times 6400\) si | M1 | FT ‘their \(V_2 = 0.8 \times V_1\)’ |
| \(V_3 = 5120\) | A1 | Implies all 3 marks |
| Scheme | Marks | Comments |
|---|---|---|
| \(V_0 = 240\,000\) \(V_{n+1} = 1.02V_n\) where \(n \geqslant 0\) | B1 | Accept \(1.02 \times V_n\) |
| (5) |