Algebra, STD1 EQ-Bank 11

A farmer in Western Australia observes that the rodent population on his property is doubling every two weeks.

A student claims that a linear model is NOT appropriate to predict the rodent population over time.

Is the student correct? Justify your answer. (2 marks)

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Show Answers Only

\(\text{Yes, the student is correct.}\)

\(\text{Correct justification could include ONE of the following:}\)

- \(\text{The rodent population is doubling every two weeks, which means it}\)
  \(\text{is increasing by a constant multiplier, not a constant amount — this}\)
  \(\text{is exponential growth, not linear.}\)
- \(\text{A linear model increases by the same amount each time period, but}\)
  \(\text{the rodent population increases by a larger amount each fortnight as}\)
  \(\text{the population grows.}\)
- \(\text{The graph of the rodent population over time would be an upsloping}\)
  \(\text{exponential curve, not a straight line.}\)
- \(\text{A linear model would significantly underestimate the rodent population}\)
  \(\text{over time.}\)

Show Worked Solution

\(\text{Yes, the student is correct.}\)

\(\text{Correct justification could include ONE of the following:}\)

- \(\text{The rodent population is doubling every two weeks, which means it}\)
  \(\text{is increasing by a constant multiplier, not a constant amount — this}\)
  \(\text{is exponential growth, not linear.}\)
- \(\text{A linear model increases by the same amount each time period, but}\)
  \(\text{the rodent population increases by a larger amount each fortnight as}\)
  \(\text{the population grows.}\)
- \(\text{The graph of the rodent population over time would be an upsloping}\)
  \(\text{exponential curve, not a straight line.}\)
- \(\text{A linear model would significantly underestimate the rodent population}\)
  \(\text{over time.}\)