106 Unit 3 Problem solving: basic skills
Commentary
Looking at the statements in turn:
A This statement explains the initial
increase in growth rate – the increase
looks exponential (increasing in size at a
constantly growing rate).
B This statement would not explain the
initial growth – it would start at a higher
growth rate, which would then decrease
all the time.
C This statement would explain the drop to
zero growth after a time, linked to a lack
of nutrient.
D There is no indication of death; in that
case the population would fall.
E If both processes were linear (resulting in
straight-line graphs), a combination of
them would also result in a straight-line
graph.Hypotheses, reasons,
3.8 Hypotheses, reasons, explanations and inference
3.8
In the introductory chapters we saw that
problems involving making inferences from
data or suggesting reasons for the nature of
variations in the data may appear in either the
critical thinking or the problem-solving
sections of thinking skills examinations.
Such examples are usually based on
quantitative (numerical or graphical) data and
may arise from such areas as finance or
science. They require analysis of the data given
in order to reach some conclusions that may
be drawn from the data or to suggest reasons
for the nature of the data.
The example below is based on a scientific
scenario. While this requires a little
understanding of basic scientific concepts,
most of the skills involved in coming to a
solution depend on clear, logical thinking.The graph shows the results of an experiment
to determine the growth of a culture of yeast
in a nutrient medium. The liquid containing
the nutrient was made up and a small amount
of yeast introduced. At regular intervals
afterwards, the solution was stirred, a small
sample taken and the concentration of yeast
measured. The graph represents a smooth
line drawn through the results.Yeast
concentrationTimeActivity
Which of the following explanations are
consistent with the shape of the curve?
(Identify as many as apply.)
A Yeast cells divide when they have
grown enough, so grow exponentially
if they have enough nutrient.
B The rate of increase of yeast cells
depends only on the amount of
nutrient.
C Eventually, the growth of yeast cells is
limited by lack of nutrient.
D Yeast cells die when there is
insufficient nutrient.
E The shape of the curve is explained by
a linear growth in yeast and a linear
decrease in nutrient.