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Date November 2019 Marks available 2 Reference code 19N.1.SL.TZ0.T_11
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number T_11 Adapted from N/A

Question

Elvis Presley is an extremely popular singer. Although he passed away in 1977, many of his fans continue to pay tribute by dressing like Elvis and singing his songs.

The number of Elvis impersonators, Nt, can be modelled by the function

Nt=170×1.31t,

where t, is the number of years since 1977.

Write down the number of Elvis impersonators in 1977.

[1]
a.

Calculate the time taken for the number of Elvis impersonators to reach 130000.

[2]
b.

Calculate the number of Elvis impersonators when t=70.

[2]
c.

The world population in 2047 is projected to be 9500000000 people.

Use this information to explain why the model for the number of Elvis impersonators is unrealistic.

[1]
d.

Markscheme

170      (A1)   (C1)

[1 mark]

a.

130000=170×1.31t      (M1)

Note: Award (M1) for equating 130000 to the exponential function.

t= 24.6  (24.5882 (years))        (A1)   (C2)

[2 marks]

b.

170×1.3170      (M1)

Note: Award (M1) for correct substitution in the function Nt.

2.75×1010 2.75067×1010, 27500000000, 27506771343        (A1)   (C2)

[2 marks]

c.

The number of Elvis impersonators in 2047, is greater than the world population.       (R1) (C1)

OR

2.75×1010>9500000000       (R1) (C1)

Note: Award (R1) for a correct comparison of their number of impersonators with the world population. Follow through from part (c) if a reasonable argument can be made that the model is unrealistic.
Award (R0) if the number of impersonators is not explicitly seen in part (c) or in part (d).

[1 mark]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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