QUESTION 42 (5 marks)
An annual survey of a bird colony begins with 750 individuals. Over one year there are 140 births, 95 deaths, 32 immigrants and 47 emigrants.
a) Calculate the net population change and the final population size. [2 marks]
b) Calculate the annual per-capita growth rate as a percentage of the initial population. [2 marks]
c) Explain why a positive net change does not establish that the population is growing exponentially. [1 marks]
Practice marking scheme
Answer
a) +30 birds; 780 birds. b) 4.0% per year. c) One interval does not establish a sustained proportional growth pattern.
Working
, giving . The per-capita annual rate is . Exponential growth involves sustained growth proportional to population size under suitable conditions; a single positive change can also occur during logistic growth.
Marking criteria
- Calculates net change as +30. [1 mark]
- Calculates final size as 780. [1 mark]
- Divides net change by the initial size. [1 mark]
- Calculates 4.0% per year. [1 mark]
- Explains why one interval cannot establish the growth mode. [1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusCompare your working with the guide above.