Food for thought

## Process/graph pairs

Here is each graph matched to its process.

• Number of rapidly dividing bacteria present in a food-limited environment, starting from a small initial sample.

The number initially increases exponentially, as the bacteria divide repeatedly, but as the number of bacteria increases the lack of food becomes an issue and so growth is much less fast.

• Concentration in the blood of a drug following an injection.

There is a high level of the drug at the start, but it then drops off exponentially as the body metabolises the drug.

• Angle of oscillation of a real pendulum of length $1$ metre in air.

The angle oscillates between two extremes, but those extremes become less extreme over time: the pendulum loses energy (through friction, for example) and so swings less far.

• Volume (in litres) against pressure (in atmospheres) for $1$ mole of an ideal gas at $0^{\circ}\text{C}$.

Volume is inversely proportional to pressure (this makes intuitive sense, a given amount of gas takes up less volume as the pressure on it increases), so we get a reciprocal curve.

• Vertical distance travelled by a small, heavy ball dropped from a plane.

If we ignore effects of air resistance and so on, the key thing is gravity, which leads to the ball experiencing constant acceleration. This gives rise to a quadratic curve.

• Rate of reaction of a catalysed reaction in terms of the concentration of reagent.

Introducing some reagent leads to a rapid increase in the rate of reaction; continuing to introduce reagent has a less dramatic effect but does still increase the rate of reaction until saturation is reached.

• Number of rapidly dividing bacteria present in a food-rich environment, starting from a small initial sample.

The number of bacteria increases exponentially.

• Hours of daylight per day in a town in the far northern hemisphere.

Over the course of a year, the number of hours of daylight will increase to a maximum in the middle of summer (just below $24$) and decrease to a minimum in the middle of winter (just above $0$) and return to its starting point.
One astronomical unit is defined to be the average distance of the Earth from the Sun. As the Earth moves round the Sun in its elliptical orbit over the course of the year, it will move from slightly larger than $1$ to slightly less than $1$ and back again.