Mathematics AI: EXPONENTIALS - LOGARITHMS Topical Past Paper Questions

[Maximum mark: 29] In this question researchers are trying to find the most accurate model to use when modelling a population of wolves. Historically, a population of wolves in an area had a stable size of 200. After some years of disruption, the population was reduced to 40 wolv…

[Maximum mark: 7] The pH scale is a measure of the acidity of a solution. Its value is given by the formula $$ \mathrm{p H}=-\log_{10}[\mathrm{H^{+}}], $$ where $ [H^{+}] $ is the concentration of hydrogen ions in the solution (measured in moles per litre). (a) Calculate the pH v…

[Maximum mark: 7] The decay of a chemical isotope over five years is recorded in Table 1. The mass of the chemical M is measured to the nearest gram at the beginning of each year t of the experiment. Table 1 It is believed that the decay of the isotope can be modelled by an equat…