SPM.1.SL.TZ0.5

pestleMathematicsAISLPaper 1SPM· sl-2-5-modelling-functionssource ↗

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 $P = 1350 + 400{\left( {1.25} \right)^{ - t}}$ , $t$ ≥ 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]

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

[1]

Markscheme / solution

1750 A1

[1 mark]

a.i.

$1350 + 400{\left( {1.25} \right)^{ - 5}}$ (M1)

= 1480 A1

Note: Accept 1481.

[2 marks]

a.ii.

$1400 = 1350 + 400{\left( {1.25} \right)^{ - t}}$ (M1)

9.32 (days (9.31885…) (days)) A1

[2 marks]

1350 A1

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

[1 mark]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]