Cambridge Additional Mathematics

9

O

lgK

lg 7

( 81lg lg, 63)

lgt

O x 3

(5 20),

y lgy

O lgx

192 Straight line graphs (Chapter 7)

a

b

10 Graph A Graph B

The relationship betweenxandyinGraph Acan also be plotted as a straight line inGraph B. For the

straight line inGraph B, find the:

a gradient b intercept on the vertical axis.

We have seen how the transformation of variables may allow us

to display a non-linear relationship using a straight line graph. It

is particularly useful to do this if we are trying to use a function

to model data.

Case study Exponential growth and decay#endboxedheading

Logarithms are particularly important in science. Many physical processes are modelled accurately by

exponential laws.

For example, the United Nations published the following data on world population:

Year PopulationP(in billions) lgP Year PopulationP(in billions) lgP

1750 0 : 79 ¡ 0 : 236 1950 2 : 52 0 : 924

1800 0 : 98 ¡ 0 : 0202 1960 3 : 02 1 : 11

1850 1 : 26 1970 3 : 70 1 : 31

1900 1 : 65 0 : 501 1980 4 : 44 1 : 49

1910 1 : 75 0 : 560 1990 5 : 27 1 : 66

1920 1 : 86 0 : 621 1999 5 : 98 1 : 79

1930 2 : 07 0 : 728 2000 6 : 06 1 : 80

1940 230 0 833 2010 679 192

E Finding relationships from data

Exponential, power, and logarithmic

models can be transformed to

straight line graphs.

0 : 231

WriteKin terms oft.

Hence findKwhen t=9.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\192CamAdd_07.cdr Tuesday, 21 January 2014 12:14:25 PM BRIAN