Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 9
1 . |
x The relationship between two variables T and x is given by T � hk
, where h , k �
|
, |
|
T � 0
.
|
|
( a ) Express lnT in terms of x .
A graph of lnT against x shows a straight line such that the gradient and the vertical intercept of the line are 0.06 and � 1.7 respectively .
[ 3 ]
( b ) Find , correct the answers to 4 decimal places , the value of
( i ) h ;
( ii ) k .
2 . The relationship between two variables W and x is given by W
W , x � 0 .
[ 4 ] k
� , where h , k � , hx
( a ) Express lnW in terms of ln x .
[ 3 ] A graph of lnW against ln x shows a straight line such that it passes through the points ( 0.3 , 0 ) and ( 0,1.5 ) .
( b ) Find the value of k .
( c ) Find the value of h , correct the answer to 4 decimal places .
[ 2 ]
[ 2 ]
3 . The relationship between two variables V and x can be modelled by lnV �3x � b , where b� , V � 0 . A graph of lnV against x shows a straight line such that the gradient and the horizontal intercept of the line are 3 and � 6 respectively .
( a ) Find the value of b .
( b ) Hence , express V in terms of x .
( c ) Find the ratio of the values of V when x increases from 0.5 to 1 .
[ 2 ]
[ 1 ]
[ 3 ]
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