Solutions to Chapter Review Extended-Response Questions
1
a
From the graph, after 20 months, the value of the machine is $200 000.
b
The line predicts that the machine will have no (zero) value after 60 months (or 5 years).
c
Choose any two points on the line, say (t1, V1) = (0, 300), (t2, V2) = (60, 0).
Then, the equation of the straight line is given by:
d
After 3 years, t = 36. So V = 300 – 5 × 36 = 120.
The value of the machine after 3 years is $120, 000.
e
The slope of the equation is –5, which indicates the machine depreciates by $5 000 per month.
2
a
From the graph, when there were 500 000 machines the amount of money transacted through
ATMs was $80 billion.
b
Choose any two points on the line, say (N1, A1) = (0, 0) and (N2, A2) = (1000, 160).
Then, the equation of the straight line is given by:
c
When there were 600 000 machines, N = 600.
When N = 600, A = 0.16 × 600 = 96.
The amount transacted when there were 600 000 machines is predicted to be $96 billion.
d
When there are 1 500 000 machines, N = 1500.
When N = 1500, A = 0.16 × 1500 = 240.
The amount transacted when there are 1 500 000 machines is predicted to be $240 billion.
e
The amount transacted through ATM machines is increasing by $0.16 billion (slope) with each
1 000 extra ATMs.
3
a
b
Choose any two points on the line, say (A1, H1) = (0, 80), (A2, H2) = (4, 105).
Then, the equation of the straight line is given by:
When A = 3, H = 6.25 × 3 + 80 = 98.75
The height of a child aged 3 is predicted to be 98.75 cm.
c
4
a
The slope is 6.25, so the equation of the line of best fit tells us that, each year, children’s heights
increase by 6.25 cm.
i When x = 20, C = 5 + 0.40 × 20 = 13.
The charge for using 20 kL of water is $13.
ii When x = 30, C = −31 + 1.6 × 30 = 17.
The charge for using 30 kL of water is $17.
iii When x = 50, C = −31 + 1.6 × 50 = 49
The charge for using 50 kL of water is $49.
b
i When you use less than 30 kL of water, the linear equation C = 5 + 0.40x is used.
The slope is 0.40, which means that a kilolitre of water costs $0.40, or 40 cents.
ii When you use more than 30 kL of water, the linear equation C = −31 + 1.6x is used.
The slope is 1.6, which means that a kilolitre of water costs $1.60.
c
The graph below is the segmented graph for 0 ≤ x ≤ 50 for the equations
C = 5 + 0.40x (0 ≤ x < 30)
C = −31 + 1.6x (x ≥ 30)