Real-life equations

Here are several equations from real life. Can you work out which measurements are possible from each equation?
Age
16 to 18
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



 


This is a list of many of the most important equations in science. In each case, we have labelled the two variable quantities $x$ and $y$. The letters $a, b$ stand for constants in each case

Constant motion $\quad\quad\quad\quad\quad a = \frac{x}{y}$

Constant acceleration $\quad\quad\quad x = uy + \frac{1}{2} ay^2$

Beer Lambert Law $\quad\quad\quad\quad a=bxy$

Exponential decay $\quad\quad\quad\quad x=a e^{by}$

Michaelis-Menton $\quad\quad\quad\quad x = \frac{ay}{b+y}$

pH $\quad\quad\quad\quad\quad\quad\quad\quad\quad x = -\log_{10}(y)$

Can you identify the possible meanings of the variables $x$ and $y$ and the constants in each case?

Real-life equations


Four graphs are shown above, where the two axes intersect at the origin $(0, 0)$.

The red crosses show four measurements. Although we do not know the numerical values (because there are no scales on the graphs), we can see whether the values are positive or negative in each variable. For example, the first measurement is positive in $x$ and positive in $y$; the second measurement is positive in $y$, negative in $x$.

For processes evolving according to each of the equations above, which measurements are possible?