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

Now

Let’s say we find our current amount of K-40 to be 1mg

And our current A-40 to be 0.01 mg

This is something we can find using normal means

We want to know “how old is this rock”

Yeah

We have this equation
1mg (current amount) = N_0*e^-kt

And we already know k

All we need is the initial amount

I see

We have 1mg, our current, plus .01/11%

Because remember, we have a certain amount of K-40 that had to decay into .01mg of Argon

And that argon is 11% of that

So .01/11% will get us the amount that decayed

Still with me?

I’m trying to get this last part

Okay

Now

Yeah

Doing some fancy maths

We can isolate t

Lol

And calculate it to be 157 million years

This