The rate at which a quantity of a radioactive substance decays is proportional to the quantity of the substance. The constant of proportionality A is called the decay constant or decay rate (A, like most physical constants, is conventionally represented by a positive number. That's why we call it a decay rate. If a quantity were increasing, we would use the words "growth rate" and also represent that by a positive number). Write the initial value problem that describes the amount N(t) of the radioactive substance remaining after time t, if the initial quantity N(O) is 5. d~=- dt X N(O) = 5 J What is the solution to the initial value problem? 53 W The half life of the substance is the time thalf at which exactly half of the substance remains. What is the half life in terms of A? 111(2) thalf = k J *.' symbolic formatting help