You are given the ratio of carbon atoms in a fossil. use the information to estimate the age of the fossil. in living organic material, the ratio of radioactive carbon isotopes to the total number of carbon atoms is about 1 to 1012. when organic material dies, its radioactive carbon isotopes begin to decay, with a half-life of about 5715 years. so, the ratio r of carbon isotopes to carbon-14 atoms is modeled by where t is the time (in years) and t = 0 represents the time when the organic material died. (round your answer to one decimal place.)