Q12 · 2022 · Technology-activeSimple familiar5 marks
QUESTION 12 (5 marks)
A scientist collects data for a species of tree frog in a protected area. Details for the female tree frog population are shown below.
| Age (years) | 0–1 | 1–2 | 2–3 | 3–4 |
|---|---|---|---|---|
| Population in Year 1 | 150 | 101 | 84 | 62 |
| Birth (breeding) rate | 0.4 | 0.7 | 0.5 | 0.1 |
| Survival rate | 0.6 | 0.3 | 0.2 | 0 |
The scientist uses a Leslie matrix model to make predictions about the female tree frog population.
a)[1 mark]
State the initial population matrix.
b)[1 mark]
Determine the Leslie matrix.
c)[3 marks]
A species is considered to be endangered if the female population in a restricted area is predicted to fall to less than 125 in the next 20 years. Determine whether this species of tree frog is considered to be endangered.
WORKED SOLUTION
5 marksQCAA guide · typeset solution
ANSWER
The species is considered endangered; the predicted Year 20 female population is approximately .
Worked solution
a) The initial population matrix is
b) The Leslie matrix is
c) Consider the population in Year 20. Using a GDC,
The female population in Year 20 is approximately . The female population is less than 125 within the 20-year period, so the species is considered to be endangered.
correctly states the initial population matrix
correctly determines the Leslie matrix
calculates a matrix representing the female population within a 20-year period
calculates female population for a year within a 20-year period
makes a suitable decision whether the species is considered endangered
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