Analysis and Approaches for IBDP Maths Ebook 1 | Page 55

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2. The number of trams and the number of people using trams in a city is studied.
The number of trams in the city after t years is modeled by the function
At ( ) �420� 1.15 t .
(a)
(b)
Find the initial number of trams.
Find the number of trams after six years.
(c) How long does it take for the number of trams to reach 750?
The number of people using trams in the city after t years is modeled by the function
4680000
Bt () �
.
kt
70e � �130
[2]
[2]
[3]
4
(d) After five years, there are 27500 people using trams. Find the value of k .
(e)
The number of trams first exceeds five times the number of people using trams
after n years, where n� . Find the value of n .
3. The number of food delivery cars and the number of people using food delivery cars in a
town is studied.
The number of food delivery cars in the town after t weeks is modeled by the function
( ) 1050 1.25 t
At � � .
(a) Find the initial number of food delivery cars.
[2]
(b) Find the number of food delivery cars after sixteen weeks.
[2]
(c) How long does it take for the number of food delivery cars to reach 4200?
[3]
The number of people using food delivery cars in the town after t weeks is modeled by
410000
the function Bt () �
.
75k�
95e �kt
[3]
[4]
(d)
(e)
After twelve weeks, there are 4600 people using food delivery cars. Find the value
of k .
[3]
The number of food delivery cars first exceeds double the number of people using
food delivery cars after n weeks, where n� . Find the value of n .
[4]
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