The radioactive substances decays exponentially. The scientist starts with 100 mg of the radioactive substance that after 6 days decayed to 60 mg. Answer following based on this information:
(a) Develop the exponential decay equation to model amount of substance remaining A(t), as the function of days, t.
(b) How long will it take to decay to 15 mg? Illustrate all algebra leading to the solutions comprising all suitable properties of logarithmic functions.
(c) How long until there is only 1.5 mg left?
(d) Find the half life of substance? That is when will exactly half original amount remain?
(e) Find end behavior of A(t) as t ! 1 ? Describe physical meaning of this behavior.
(f ) Determine the domain and range of function?
(g) Make the graph of function, label axes and points from prompt also those found in parts b and d.