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| Reduction
to linear form |
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Reduction
to linear form
1. The table below shows the values
of y obtained experimentally for the given values
of x. Show that there is
a relation of the form  and
find approximate values of k and n.
x
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4
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8
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15
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19
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24
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y
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2.45
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2.60
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2.80
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2.89
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3.00
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2. The variables
x and y below are believed to be related by a law
of the form  where a and b are
constants. Use Excel to show that this is so and
determine the probable values of a and b.
x
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1
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2
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3
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4
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5
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6
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y
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-1.897
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0.588
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1.599
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2.262
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2.757
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3.153
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3. The following values of x and y
are believed to obey a law of the form  where a,
b and c are
constants. Show that they do obey this law and hence
estimate the value of the ratios a:b:c.
x
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0
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1
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2
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3
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4
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y
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1.00
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0.67
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0.50
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0.40
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0.33
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4. It is thought that two variables
s and t satisfy a relation of the form  where
the constants a and b are
positive integers. Show by using Excel that this
is supported by the following table of measured values,
and find the values of a and b.
t
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0.2
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0.4
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0.6
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0.8
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1
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s
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1.09
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1.96
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2.67
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3.22
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3.64
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