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Date May Specimen paper Marks available 2 Reference code SPM.1.SL.TZ0.5
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number 5 Adapted from N/A

Question

Professor Vinculum investigated the migration season of the Bulbul bird from their natural wetlands to a warmer climate.

He found that during the migration season their population, P could be modelled by P = 1350 + 400 ( 1.25 ) t , t ≥ 0 , where t is the number of days since the start of the migration season.

Find the population of the Bulbul birds at the start of the migration season.

[1]
a.i.

Find the population of the Bulbul birds after 5 days.

[2]
a.ii.

Calculate the time taken for the population to decrease below 1400.

[2]
b.

According to this model, find the smallest possible population of Bulbul birds during the migration season.

[1]
c.

Markscheme

1750     A1

[1 mark]

a.i.

1350 + 400 ( 1.25 ) 5     (M1)

= 1480    A1

Note: Accept 1481.

[2 marks]

a.ii.

1400 = 1350 + 400 ( 1.25 ) t        (M1)

9.32 (days (9.31885…) (days))   A1

[2 marks]

b.

1350   A1

Note: Accept 1351 as a valid interpretation of the model as P = 1350 is an asymptote.

[1 mark]

c.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions

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