MATH VCE MATHEMATICAL METHODS Unit 3
APPLICATION TASK SAC 2019
The Bilby Population
SESSION 2 of 4
SAC Details:
This SAC is designed to assess Outcome 1, Outcome 2 and Outcome 3 from the following Areas of
Study an
...
MATH VCE MATHEMATICAL METHODS Unit 3
APPLICATION TASK SAC 2019
The Bilby Population
SESSION 2 of 4
SAC Details:
This SAC is designed to assess Outcome 1, Outcome 2 and Outcome 3 from the following Areas of
Study and will contribute 50 % of the marks for Unit 3 and 4 SAC work combined
Functions and Graphs
Algebra of Functions
Differential Calculus
Outcome 1 Total 15 marks
Define and explain key concepts as specified in the content from the areas of study, and apply a
range of related mathematical routines and procedures.
Outcome 2: Total 20 Marks
Apply mathematical processes in non-routine contexts, and analyse and discuss these applications
of mathematics.
Outcome 3 Total 15 Marks
Select and appropriately use a computer algebra system and other technology to develop
mathematical ideas, produce results and carry out analysis in situations requiring problem-solving,
modelling or investigative techniques or approaches.
Page 1 of 7
De La Salle College Mathematical Methods Application Task 2019
SAC Conditions:
You are allowed the USE of CAS Technology and a BOUND Reference book for the entire SAC
Loose sheets of papers do not constitute a reference book and will be confiscated
No Mobile phones or any other electronic items are permitted in the SAC room
No discussion or talking is permitted during the SAC
Do not write the CAS syntax as part of your answers
When not specified, express your answer in exact form / value (an approximated answer may
result in loss of mark).
All Graphs must include all key features that describe the graph.
Page 2 of 7
De La Salle College Mathematical Methods Application Task 2019
Analysis of Bilby Populations in the Kimberley
The population model of the Lennard River Bilby in the Kimberley PL is given by the equation;
PL (t) =
300
1+e-( t-30 ) +20
Another colony of Fitzroy River Bilby has a population PF given by the model;
PF (t) =
150
1+e-( t-10 ) +10
In these models both populations are measured in numbers of Bilbies and t is measured in months
from the present.
Unfortunately for the researchers, and the Bilby, 1 month into the 4 year program, a virus was
transmitted on the boots of the researchers between both colonies. Thus both colonies were
infected on the same day. After much research, they were able to establish that the virus killed
their hosts (the Bilby) in each colony according to the equation:
PV (t )=15loget
Where PV gives the number of infected Bilby over the same time interval t months.
Unfortunately, any infected Bilby does not survive.
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