How would I calculate the age of a rock only given the amount of each in grams and half-life?

Question

40K decays to 40Ar.
Half life of 40K is 1.25 billion years.
40K = 20 grams
40Ar= 5 grams

I think the formula is
Final Amount of 40K = Initial Amount of 40K * (1/2)^(time/half-life)

If I plug in the values I still don't have a value for time. And where would the grams of 40Ar fit in?

Answer 1

You started with 25 grams, you now have 20 grams

20=25(1/2)^(t/th)

.8=(1/2)^halflives

log both sides...

log (.8)=halflives*log.5
halflivees= log(.8)/log(.5)

time= 1.25billion* log(.8)/log(.5)