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18.6 Practical graphs

18.6 Practical graphs

When you solve a real-life problem, you may need to use a function where the graph is a straight line.
In this topic, you will investigate some real-life problems.

Worked example 18.6

The cost of a car is $20 000. The value falls by $1500 each year.
a Write a formula to show the value (V ), in thousands of dollars, as a function of time (t ), in years.
b Draw a graph of the function.
c When will the value fall to $11 000?

a V = 20 − 1.5 t When t = 0, V = 20.
V decreases by 1.5 every time t increases by 1.
b V Plot a few values to draw the graph.
25 Use V and t instead of y and x.
Negative values are not needed.
The gradient is −1.5.
20
Value (thousands of $) 15

10

5

0 t
2 4 6 8 10
Time (years)
c After 6 years The value of t when V = 11

In the worked example, the gradient is −1.5. "is means that the value falls by $1500 dollars each year.
) Exercise 18.6

1 A tree is 6 metres high. It grows 0.5 metres each year.
a Write down a formula to show the height (y), in metres, as a function of time (x), in years.
b Draw a graph of the formula.
c Use the graph to find:
i the height of the tree after 5 years ii the number of years until the tree is 10 metres high.
2 A candle is 30 centimetres long. It burns down 2 centimetres every hour.
a Write down a formula to show the height (h), in centimetres, as a function of time (t), in hours.
b Draw a graph to show the height of the candle.
c Use the graph to find:
i the height of the candle after 4 hours ii the time until the candle is half its original height.

3 The cost of a taxi is $5 for each kilometre.
a Write down a formula for the cost (c), in dollars, in terms of the distance (d), in kilometres.
b Draw a graph to show the cost.
c Use the graph to find: i the cost of a journey of 6.5 kilometres ii the distance travelled for $55.
174 18 Graphs 18 Graphs