3. A radioactive material decays so that the amount of material remain- ing at time i, Aft), is given by A(t) = Age-\"m where A0 is the amount of material present initially and t is measured in hours. Find the rate of change of the amount of material remaining with For additional help see the Mathematics Education Support Hub (MESH) www.m'est-ernsydney. edu.a11/mesll respect to t. that is nd % and show that the amount of material remaining satises the equation a _ d: _ This is known as a differential equation. What is the value of k in this raga? kA