Now, we can get to the fun part

It would be easier if I could send pictures

Yeah I guess

We can take our original equation, N_0 times e^-kt = N(t)

Checked, it's Ca-40 from beta decay of K-40

I’ll have to read up on that then

K-40 to Ar-40 is by electron capture

It’s irrelevant to this discussion though

All we care about is Argon 40

I shall keep my mouth shut then

@PhumoZTYPE

Yeah

I’m listening

We can plug in 1.25B to our equation for t

And set it equal to 1/2 N(t)

Why lol

Because in 1.25 billion years, we’ll have half the amount of K-40

Oh yess

N(t) is the amount of K-40

So we have 1/2 N_0=N_0 e^-k*1.25B

But isn’t that based on the assumption that potassium 40 is like that

Why?

It has been measured

No no

We don’t even need to measure it

We can actually calculate the initial amount

How

I’ll show you

Bare with me

I’m trying yeah

We have So we have 1/2 N_0=N_0 e^-k*1.25B

Which is half the initial amount

We can divide N_0 on both sides

Yeah

To get 1/2 = e^-k*1.25B

Apply ln to both sides

Or the natural logarithm

This’ll get you ln(1/2)= -k*1.25B

Divide -1.25 B and you get k= ln(1/2) / -1.25B

Are you still with me?

Yup