Apps. and Interpretation for IBDP Maths Ebook 1 | Page 79

Exercise 22
1. Kensuke purchased a new car for 24000 EUR on 1st January, 2011 and insures his car
with an insurance company. In 2011, Kensuke needs to pay 1200 EUR for the insurance
premium, and the amount he needs to pay is reduced by 15 EUR per year.
(a) Find the amount of insurance premium Kensuke has paid in 2014.
[2]
The insurance company also estimates the value of Kensuke’s car in each year. The
company estimates that the car depreciates by 15% each year, such that the value of his
car is 20400 EUR in 2012.
(b) Find the exact value of the car in 2016.
[2]
(c) Find the year when the value of the car is first below 8000 EUR.
[3]
Kensuke will stop insuring his car if the amount of insurance premium is greater than the
value of the car in a particular year.
(d)
(e)
Find the year when Kensuke stops insuring his car.
Hence, find the total amount of insurance premium Kensuke has paid in this
period.
[3]
[3]
8
2. The table below shows the first four terms of four sequences: t n
, u
n
, v
n
and
w
n
.
n 1 2 3 4
t
n 50 100 200 400
u
n 50 70 110 170
v
n 50 1050 2050 3050
w
n 50 50 50 50
(a)
State the sequence which is
(i)
(ii)
(iii)
(iii)
arithmetic;
geometric;
neither arithmetic nor geometric;
both arithmetic and geometric.
[4]
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