The rock is approximately how many billion years old.

Question

A certain element has a half life of

1.5

billion years.

a. You find a rock containing a mixture of the element and lead. You determine that

45​%

of the original element​ remains; the other

55​%

decayed into lead. How old is the​ rock?

Answer 1

1/2= e^1.5r where r = rate of decay

take natural logs of both sides, solve for r

ln.5 = 1.5r

r = (ln.5)/1.5 = rate of decay

45% remains when

45/100 = 9/20 = e^(ln.5)t/1.5

take natural logs

ln.45 = ln.5)(t)/1.5

t = 1.5ln.45/ln.5 = about 1.728 billion years rounded off to 3 decimals

when only 45% remains

55% decayed into lead when 45% remains, so same 1.728 billion years

(this looks like part 2 is a trick question)