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Example
Paper 1 – Semi-Log and Log-Log Models
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The relationship between the air pressure Pt () ( in Pa ) in an instrument , Pt ( ) � 10 , and kt the time t minutes after the start of the experiment is given by P( t) �10
� he , where h , k � .
( a ) Express ln ( P � 10 ) in the form at � b.
A graph of ln ( P � 10 ) against t shows a straight line such that the gradient and the vertical intercept of the line are 0.015 and 2.8 respectively .
( b ) Write down the value of k .
( c ) Find the value of h , correct the answer to 4 decimal places .
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Solution
( a ) P �10
� he
P �10
� he kt
kt kt ln ( P �10 ) � ln ( he ) ( A1 ) for correct approach ln ( P �10 ) � ln h � ln e kt ( A1 ) for correct approach ln ( P �10 ) � kt � ln h
A1
( b ) 0.015 A1
( c ) ln h � 2.8 h e h � 16.44464677 h � 16.4446
A1
2.8
� ( M1 ) for valid approach
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