| Date | May 2017 | Marks available | 3 | Reference code | 17M.1.sl.TZ2.14 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 14 | Adapted from | N/A |
Question
Jashanti is saving money to buy a car. The price of the car, in US Dollars (USD), can be modelled by the equation
\[P = 8500{\text{ }}{(0.95)^t}.\]
Jashanti’s savings, in USD, can be modelled by the equation
\[S = 400t + 2000.\]
In both equations \(t\) is the time in months since Jashanti started saving for the car.
Jashanti does not want to wait too long and wants to buy the car two months after she started saving. She decides to ask her parents for the extra money that she needs.
Write down the amount of money Jashanti saves per month.
Use your graphic display calculator to find how long it will take for Jashanti to have saved enough money to buy the car.
Calculate how much extra money Jashanti needs.
Markscheme
400 (USD) (A1) (C1)
[1 mark]
\(8500{\text{ }}{(0.95)^t} = 400 \times t + 2000\) (M1)
Note: Award (M1) for equating \(8500{(0.95)^t}\) to \(400 \times t + 2000\) or for comparing the difference between the two expressions to zero or for showing a sketch of both functions.
\((t = ){\text{ }}8.64{\text{ (months) }}\left( {8.6414 \ldots {\text{ (months)}}} \right)\) (A1) (C2)
Note: Accept 9 months.
[2 marks]
\(8500{(0.95)^2} - (400 \times 2 + 2000)\) (M1)(M1)
Note: Award (M1) for correct substitution of \(t = 2\) into equation for \(P\), (M1) for finding the difference between a value/expression for \(P\) and a value/expression for \(S\). The first (M1) is implied if 7671.25 seen.
4870 (USD) (4871.25) (A1) (C3)
Note: Accept 4871.3.
[3 marks]
