Exercise 8
1 . In an experiment , the amount of bacteria Bt ()( in million ) in a culture t hours after 1 a . m . 12 on the first day can be modelled by Bt () � , t � 0 .
0.06t
1 � 5e �
2
( a ) Find the amount of bacteria at
( i ) 1 a . m . on the first day ;
( ii ) 3 a . m . on the second day .
( b ) Write down the range of Bt ().
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2 . The weight of a substance Wt ()( in gram ) t days after 1st July can be modelled by 27 Wt () � , t � 0 .
0.11t
1 � 8e �
( a ) Find the weight of the substance on 1st July .
( b ) Find the date that the weight of the substance first reaches 20g .
( c ) Write down the horizontal asymptote of the graph of Wt ().
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3 . The population Pt () of a city t years after 1st January , 2010 can be modelled by 600000
Pt () � , where C � , t � 0 . It is given that P( 0 ) � 100000 .
0.11t
1 � Ce �
( a ) Find C .
( b ) Hence , find t when Pt ( ) � 450000 .
( c ) Write down the horizontal asymptote of the graph of Pt ().
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