Final answer:
A residuals plot from a linearised exponential model using logs helps in identifying exponential relationships as linear trends on a log-log plot, demonstrating the utility of logarithmic scales in simplifying complex relationships in various fields such as chemistry and population dynamics.
Step-by-step explanation:
When a residuals plot comes from an exponential model linearised using logs, it indicates that the data has been transformed to linearize the exponential relationship. If you observe a log-log plot, this means both axes are plotted on a logarithmic scale. This is exceptionally useful for representing data over several orders of magnitude, as exponential functions and relationships, such as those in equilibrium calculations or the rate of decay in radioactive substances, display as straight lines under logarithmic transformation. Hence, on a logarithmic plot, trends resembling an exponential growth or decay are easily identifiable as linear trends. This reflects the exponential relationship, such as population or energy growth or the concentration of reactants in a chemical reaction over time.
For example, in a first-order reaction in chemistry, the concentration of reactants does not decrease linearly over time. However, when the natural logarithm of reactant concentration is plotted against time, it results in a linear relationship, indicating a first-order reaction. Similarly, growth models of populations can be exponential (J-curve) or logistic (S-curve), and the correct model can help in understanding the dynamics of population growth.