2 . The number of elephants P in a small jungle is modelled by P()
t � a � b� c �t , where t is the number of years after 1 st January , 2019 , and a , b and c are constants .
It is given that there are 116 elephants on 1 st January , 2019 .
( a ) Find an equation connecting a and b .
There are 172 elephants on 1 st January , 2020 .
( b ) Find the another equation connecting a , b and c .
c satisfies the equation logc81 � 4 .
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( c ) ( i ) Show that c � 3.
( ii ) Hence , find a and b . [ 5 ]
( d ) Find the number of elephants on 1 st January , 2022 , giving the answer correct to the nearest integer .
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( e ) Write down the minimum value of the upper bound of the number of elephants .
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( f ) Find the number of years needed after 1 st January , 2019 when the number of elephants first exceeds 195 .
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( g ) Someone claims that the amount of time when the number of elephants is between 170 and 180 is the half of that when the number of elephants is between 180 and 190 . Is the claim correct ? Explain your answer .
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