18M.1.SL.TZ1.T_9

pestleMathematicsAISLPaper 118M· sl-2-5-modelling-functionssource ↗

In an experiment, a number of fruit flies are placed in a container. The population of fruit flies, P , increases and can be modelled by the function

$P\left( t \right) = 12 \times {3^{0.498t}},\,\,t \geqslant 0,$

where t is the number of days since the fruit flies were placed in the container.

Find the number of fruit flies which were placed in the container.

[2]

a.i.

Find the number of fruit flies that are in the container after 6 days.

[2]

a.ii.

The maximum capacity of the container is 8000 fruit flies.

Find the number of days until the container reaches its maximum capacity.

[2]

Markscheme / solution

$12 \times {3^{0.498 \times 0}}$ (M1)

Note: Award (M1) for substituting zero into the equation.

= 12 (A1) (C2)

[2 marks]

a.i.

$12 \times {3^{0.498 \times 6}}$ (M1)

Note: Award (M1) for substituting 6 into the equation.

320 (A1) (C2)

Note: Accept an answer of 319.756… or 319.

[2 marks]

a.ii.

$8000 = 12 \times {3^{0.498 \times t}}$ (M1)

Note: Award (M1) for equating equation to 8000.
Award (M1) for a sketch of P(t) intersecting with the straight line y = 8000.

= 11.9 (11.8848…) (A1) (C2)

Note: Accept an answer of 11 or 12.

[2 marks]

Examiners’ report

[N/A]

a.i.

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a.ii.

[N/A]