Solved: Professor Vinculum investigated the migration season of the Bulbul bird from... [IB Mathematics Applications & Interpretation (Math AI)]

Professor Vinculum investigated the migration season of the Bulbul bird from their naturalwetlands 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 themigration season.

Question

SLPaper 1

Professor Vinculum investigated the migration season of the Bulbul bird from their naturalwetlands 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 themigration season.

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

[1]

Verified

Solution

1750 A1

[1 mark]

Find the population of the Bulbul birds after 5 days.

[2]

Verified

Solution

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

= 1480 A1

Note: Accept 1481.

[2marks]

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

[2]

Verified

Solution

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

9.32 (days (9.31885…) (days)) A1

[2marks]

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

[1]

Verified

Solution

1350 A1

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

[1 mark]

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