7. [4 marks] A radioactive isotope decays exponentially over time. The amount of the substance remaining after hours is given by the function 1% 40 =4:(3) where 4, is the initial amount of the isotope and & is the half-life in hours. a) Write the function A(t) if the initial amount is 500 g and the half-life is 10 hours. b) Write the function 4'(t) that models the rate of change of the amount of the isotope. c) Determine the time t at which the rate of change will be 2.5 g/h