From this task you should appreciate that the growth rates of certain organisms over variable time scales can be strikingly different!

The blue curve represents a situation of exponential growth. For example the multiplication of a bacterium such as E. Coli over time would follow such a trend provided that adequate nutrition is available over the timescale of the experiment. The trend could be represented by the form 2$^{\frac {t}{T}}$, where t is time and T is the period of division. Bacterial division does not occur entirely in synchrony and so a smooth curve is produced, rather than the stepped graph that would be observed during synchronised division.

The red curve is seen to represent the seasonal pattern of plant growth which is rapid during the spring and relatively stagnant during autumn and winter. It is also seen that year upon year, the rate of growth in the fast growth period (seen as 'steps') increases.
What do you think would happen to the shape of the growth curve of an oak tree once it has reached maturity?

The brown curve depicts the growth of a crustaceans or arthropods. There are many examples of organisms that fit this curve. A few are tarantulas, lobsters and crabs. Crustaceans have a cuticle that is often biomineralised with substances such as calcium carbonate to produce a rigid exoskeleton. However this inhibits growth; the exoskeleton must be shed through a process known as moulting. Intake of water facilitates the rapid expansion of the softer new cuticle before it hardens after the old cuticle is detached. This process is depicted by the vertical 'step' portions within the growth curve. Internal tissue growth occurs constantly.
Why might the moulting period be a dangerous time for an organism such as a shore crab?

The black curve represents classical mammalian growth. The initial portion of the curve depicts the rapid growth of a new-born infant. This growth rate falls and then progressively increases during adolescence. Eventually a stage of maturity is reached where mitotic processes operate on the whole to replenish cells within the individual.

As an extension, 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?