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18.6 Practical graphs

4 There are six cars in a car park. Every minute another two cars enter the car park. No cars leave.
a Write down a formula to show the number of cars (y) in the car park after t minutes.
b Draw a graph to show the number of cars in the car park.
c Use the graph to find:
i the number of cars after 5 minutes ii the time before there are 24 cars in the car park.
d The car park only has spaces for 24 cars. Show this on the graph.
5 Anders has $20 credit on a mobile phone. Each text costs $0.50.
a Write down a formula for the credit (c), in dollars, after sending t texts.
b Draw a graph to show the credit.
c Anders sends 11 texts. How much credit is left?

6 The population of an animal in a wildlife reserve is 8000. The population decreases by 500 each year.
a Write a formula to show the population (P) as a function of the number of years (Y).
b Draw a graph to show how the population changes over time.
c Use your graph to find the population after four years. P
d How long will it be until the population is halved? 18
16
7 This graph shows the predicted population of a country.
a What is the population now? 14
b Find the estimated population in 30 years’ time. 12
c Work out the gradient of the graph. Population (millions) 10
d Find a formula for P as a function of t. 8
6
8 Sasha puts $2000 in a bank. The bank pays her $50 every year. 4
a Work out a formula for the amount she has in dollars (A) after t years. 2
b Draw a graph to show how her money increases.
c How much does she have after five years? 0 10 20 30 40 t
d How long is it until she has $2600? Years from now

Summary

You should now know that: You should be able to:
+ An equation of the form y = mx + c gives a straight- + Construct tables of values and plot graphs of
line graph. linear functions, where y is given implicitly in
+ The value of m is the gradient of the line. It can be terms of x, rearranging the equation into the form
positive or negative. y = mx + c.
+ You can use graphs to solve simultaneous equations. + Know the significance of m in y = mx + c and find
the gradient of a straight-line graph.
+ Real-life problems can give rise to straight-line
graphs. + Find the approximate solution of a pair of
simultaneous equations by finding the point of
+ You can draw a straight-line graph accurately by intersection of their graphs.
using a table of values.
+ Construct functions arising from real-life
problems; draw and interpret their graphs.
+ Manipulate algebraic expressions and equations.
+ Draw accurate mathematical graphs.
+ Recognise connections with similar situations and
outcomes.

18 Graphs 18 Graphs 175