Apps. and Interpretation for IBDP Maths Ebook 1 | Page 49

Exercise 12
8
1. The price $P of a new car made in Germany is modelled by P( t) 2000 16000e � t
� � ,
where t is the number of years after the car is purchased.
(a) State the price of the car at the time it is purchased.
[1]
(b) Find the price of the car after 6 years.
[2]
(c) Find the time taken for the price of the car falls below $7000.
[2]
(d) Write down the maximum value of the lower bound of the price of the car in the
long run.
[1]
5
25
2. The number of bacteria N in an experiment box is modelled by N( t) �115 � 155e
,
where t is the time in days from the start of the experiment.
t
(a)
(b)
Write down the number of bacteria at the beginning of the experiment.
Find the increase in the number of bacteria in the first week, giving the answer
correct to the nearest integer.
The maximum capacity of the experiment box is 1200 units of bacteria.
[1]
[2]
(c)
Find the number of days for the experiment box to reach its maximum capacity.
[2]
3. The price EUR P of a computer system is modelled by P( t) � 90 � A� 0.7 t , where A is
a constant and t is the age of the computer measured in years. The initial price of the
computer system is EUR 840.
(a) Interpret the term (90 � A)
represents in this context.
[1]
(b) Find the value of A .
[2]
(c) Find the time when the price of the computer system drops to half of the initial
price.
[2]
(d) Write down the maximum value of the lower bound of the price of the computer
system in the long run.
[1]
www.seprodstore.com
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