### Why do this problem?

This problem encourages students to get into the real meaning of graphical representation without getting bogged down in algebraic calculations or falling back into blind computation. It will also encourage the students to think about the various differences and similarities between growth processes in the sciences.

### Possible approach

This problem works well in group discussion. For each idea, try to encourage students to explain their reasoning as precisely and clearly as possible. You could split the class into different groups and see who can produce the most valid examples for each graph.

### Key questions

• How many 'growth processes' in science can you think of. Would any of these graphs match those processes?
• How might you label the scales for each example?

### Possible extension

This type of problem is rich with extension possibilities. We suggest two:

Extension 1: Are there other shapes of graph which could be used to model other natural growth processes?

How might you describe these curves algebraically? Can you write down equations, the graphs of which match the shape of the curves in this question?

Extension 2: Look up the profile of a biphasic bacterial growth curve and understand the conditions that produced such a curve. Wikipedia is a useful place to start. Two clear phases of growth are seen due to:

1) The depletion of glucose from the nutrient medium
2) Transcription of $\beta$-galactosidase and associated enzymes to allow lactose metabolism

Is there any similarity to some of the curves given to you in the question?

You might naturally try Real-life equations next.

### Possible support

Let students leaf through a science textbook searching for graphs and charts. Do they notice that the same shapes of charts appear frequently? Can they match any to the graphs in this question?