Cambridge Additional Mathematics

10 000

20 000

30 000

40 000

50 000

V

O 1234 567 8910 t

1

2

3

4

5

lgV

O 1234 567 8910 t

176 Straight line graphs (Chapter 7)

Opening problem #endboxedheading

t(years) 1 3 5 8 10

V (dollars) 42 900 28 000 18 500 9800 6400

This table shows the value $Vof Doug’s

father’s cartyears after purchase.

Doug is trying to work out the equation connectingV

andt. When he plots the values on a graph, the result

is a curve:

Doug’s father suggests that he plots lgV againstt.

When Doug does this, the result is a straight line:

t 1 3 5 8 10

lgV 4 : 63 4 : 45 4 : 27 3 : 99 3 : 81

Things to think about:

a Is it easier to find the equation of a curve or a straight line?

b How can Doug use the equation of the straight line to determine the relationship betweenVandt?

BACKGROUND KNOWLEDGE

You should be familiar with the following facts involving points and lines on the coordinate plane:

Distance between two points

Thedistancebetween A(x 1 ,y 1 ) and B(x 2 ,y 2 ) is

d=

p

(x 2 ¡x 1 )^2 +(y 2 ¡y 1 )^2.

Midpoint

If A is (x 1 ,y 1 ) and B is (x 2 ,y 2 ),

then the midpoint of AB is

M

³x

1 +x 2

2

,

y 1 +y 2

2

́

.

B,(x y ) 22

A,(x y ) 11

d

B,(x y ) 22

A,(x y ) 11

M

cyan magenta yellow black

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100 100
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100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\176CamAdd_07.cdr Thursday, 3 April 2014 5:44:12 PM BRIAN