Unit 4
5 marks · NormalA student buys a computer for $1200. The value of the computer depreciates by 10% per year. The computer's manufacturer displays this depreciation over time using a graph.
Calculate the value of the computer after 2 years. Give your answer to the nearest dollar.
Write the formula the manufacturer could use to display the value V (in dollars) of the computer after t years, starting from $1200.
On the axes below, sketch the graph of V against t for 0≤t≤4, showing the value at t = 0, 2, and 4 years. Label your axes.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 972 $
(b) V = 1200 × (0.9)^t
(c) — · must show axes correctly labelled, points correctly plotted or marked at t = 0, 2, 4
Must show: Graph must mark 3 main points and show correct shape.
Common mistakes: Using simple not compound depreciation; mixing up x and y axis labels
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses correct multiplying factor for 10% annual decrease: (0.9)^2 × 1200.
A1 (a) · 1 mark · Correct final value, rounded to nearest dollar (972). (follow-through)
B1 (b) · 1 mark · Gives formula V = 1200 × (0.9)^t.
B2 (c) · 2 marks · Axes clearly labelled (V and t), correct positions for V=1200 at t=0, V=972 at t=2, V=787 at t=4, smooth exponential decay shape.
Worked solution
(a) Value after 2 years: V = 1200 × (0.9)^2
(b) General formula: V = 1200 × (0.9)^t
(c) On the graph, plot points (0,1200), (2,972), (4,787) and draw the smooth curve. Label axes for time t (years) and value V ($).