# Thread: applied de involving decay process

1. ## applied de involving decay process

A radioactive material, for example the isotope carbon-14, disintegrates at a rate proportional to the amount currently present. Let W(t) be the amount present at time t, measured in days, and r be the proportionality constant, the decay rate.

(a) Write a differential equation to describe the decay process.
(b) If 100 mg of carbon-14 decays to 82.04 mg in one week, determine the decay rate, r.
(c) Find an expression for the amount of carbon-14 present at any time, t.
(d) Find the time required for the thorium to decay to one-half its original amount.

i know that the de :

dW/dt = -k dt

and W(t) = A e-kt

but i dunno how to solve (b), (c) and (d)....

pls help me....

W(t) = A e-kt

you only need to replace A for the initial amount of thorium (if there is one)

b) is just solving 2 equations
1st - the initial quantity is 100 W(0)=100
2nd - the quantity at time t is 82.04 W(....

d) is solving the equation
the quantity at time t is A/2