Analysis and Approaches for IBDP Maths Ebook 1 | Seite 183

Front Page
Exercise 61
1. The number of insects, n , after t months is given by
0.28t
n � .
300e
(a) Find the value of n when t � 0.
(b) Find the rate at which n is increasing when t � 6.
[2]
(c) After k months, the rate of increase in n is greater than 1000 insects per month.
Find the least value of k , where k � .
[4]
[2]
14
2. The volume of an object, V , t seconds after the start of an experiment is given by
V t 100 t
2
� � , for 0 t 10
� � .
(a) Find the value of V when t � 10 .
(b) Find the rate at which V is increasing when t � 1.
(c)
Within k seconds after the start of the experiment, the rate of increase in V is
smaller than 30 per second. Find the greatest value of k , where k � .
[2]
[2]
[4]
3. The population of sheep in a farm, p , t months after 1 January 2019 is given by
p� 250sin(2t� 3.9) � 750 .
(a) Find the number of sheep in the farm on 1 June 2019.
[3]
(b) After n days, the rate of increase in p is equal to 0 per month for the first time.
Find the value of n , where n� .
[4]
4. The population of wolf in a forest, w , t months after 1 April 2008 is given by
w�145cos(0.5 t�5.2) � 1020 .
(a)
(b)
Find the number of wolves in the forest on 1 May 2009, correct the answer to the
nearest integer.
[3]
Assume that there are 30 days per month. After n days, the rate of increase in w
attains its maximum for the first time. Find the value of n , where n� .
[4]
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