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Question

determine a general formula that will relate A (the amount of any material that undergoes radioactivity decay) to T (the time) given that you start with A0 grams of the material and that the half life of the decaying material is given by as Th

C-14 has a half-life of 5568 years

The answer is Th=A0(1/2)^(t/h) h stands for halflife

Can anyone explain to me why? in easy steps please

Answer 1

At t = 0 the amount of material is A0. At t = h, the amount of material you want left is Ao/2. Now at t = 0
(1/2)^(t/h) = (1/2)^0 = 1 and at t = h
(1/2)^(t/h) = (1/2)^1 = 1/2

HTH ☺

Doug

Answer 2

i kinda thought it would be an exponential decay
but in your case, your given A0 how much you had to start with
and the other information you have is the half life
so you know when t = h, you should have 1/2 of A0
and when you put it all together,
you get Th = A0 (0.5)^(t/h)

Answer 3

quick and easy
You must solve the simple differential equation that governs all this.
dA/dt=tau*A
dA/A=tau*dt
integrate
A=C*exp(tau*t)
for t=0 => A0=C
A=A0*exp(tau*t)
A=A0/2
ln(1/2)=tau*t
t=ln(1/2)/tau

you extract from there whatever you need.
This is the standard way.
I use my own notations but you will interpret them fast and easy!