Apps. and Interpretation for IBDP Maths Ebook 1 | Page 206

Your Practice Set – Applications and Interpretation for IBDP Mathematics
(c)
Write down the value of the minimum average cost.
[1]
2. In an experiment about bacterial growth, the population of bacteria (in million) in a test
tube can be modelled by
P t � t � t � t � , where t is the number of days
3 2
( ) 12 36 0.001
after the start of the experiment. The experiment ends after one week.
(a)
Write down the initial amount of bacteria.
(b) Find P� () t .
It is given that P(7) � 7.001 .
[1]
[2]
(c)
(d)
Find the number of days after the start of the experiment when the population of
bacteria reaches its maximum.
[3]
Write down the value of the maximum population of bacteria.
[1]
3. The temperature Q of a substance at time t is given by
t � 0.
2 216
Q( t) � 4t
�120
� , where
t
(a) Find the t -intercepts of Q .
(b) Find Q� () t .
(c)
[2]
Find the value of t when the temperature of the substance reaches its minimum.
[3]
[3]
4. The price P of a share at time t is given by
3 2
P( t) � �t �9t � 24t
� 720 , where 0�t
� 3.
(a) Find P� () t .
(b)
Find the value of t when the price of the share reaches its minimum.
(c) State the reason why the price of the share cannot be lower than $690.
[2]
[3]
[1]
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