Geologists sometimes measure the age of rocks by using “atomic clocks.” By measuring the amounts of potassium-40 and argon-40 in a rock, the age t of the specimen (in years) is found with the formula

where A and K, respectively, are the numbers of atoms of argon- 40 and potassium-40 in the specimen.
(a) How old is a rock in which A = 0 and K > 0?
(b) The ratio A/K for a sample of granite from New Hampshire is 0.212. How old is the sample?

(c) Let A/K = r. What happens to t as r gets larger? Smaller?

Transcribed Image Text:

t = (1.26 × 10º) In[1 + 8.33(A/K)] In 2