Analysis and Approaches for IBDP Maths Ebook 1 | Page 182

Your Practice Set – Analysis and Approaches for IBDP Mathematics
61
Paper 2 Section A – Rate of change
Example
The number of bacteria, n , in a dish, after t minutes is given by
0.08t
n � 1200e .
(a) Find the value of n when t � 0.
(b) Find the rate at which n is increasing when t � 24.
(c)
After k minutes, the rate of increase in n is greater than 20000 bacteria per
minute. Find the least value of k , where k � .
[2]
[2]
[4]
Solution
(a) n (0)
0.21(0)
� (A1) for substitution
1200e
� 1200(1)
� 1200
A1 N2
[2]
(b) n� (24)
(M1) for finding derivative
� 654.81201
� 655
A1 N2
[2]
(c) n�( k) � 2000
A1
0.08k
1200(e )(0.08) 2000
0.08 125
e
k �
6
0.08 125
� M1
e k � � 0
6
k � 37.956928
(A1) for correct value
Thus, the least value of k is 38. A1 N2
[4]
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