A radioactive isotope has an initial mass of 20 g. After 5 days its mass is found to be 12 g. The rate of decay is proportional to the amount present at any instant.
(i) Write the differential equation that models the decay and state its general solution.
(ii) Using the given data, determine the decay constant k (correct to four decimal places).
(iii) Calculate the mass that will remain after 12 days (give your answer correct to two decimal places).
(iv) Find the half-life of the isotope, correct to one decimal place.