A cypress beam found in the tomb of Sneferu in Egypt contained 55% of the radioactive carbon-14 (C-14) that is found in living cypress wood. It is well-known that the half life of C-14 is...

A cypress beam found in the tomb of Sneferu in Egypt contained 55%
of the radioactive carbon-14 (C-14) that is found in living cypress wood. It is
well-known that the half life of C-14 is approximately 5,600 years.
(a) Write the initial-value problem that models this scenario using an appropriate
differential equation and initial condition.
(b) Show that the general solution of the IVP from part a) is given by A(t) = Cekt,
where A(t) is the amount of radioactive C-14 at any time t, and determine the
particular solution.
(c) Determine the approximate age of the tomb. For your answer, use a complete
statement and appropriate units.