If the half-life is t, then every t days, the amount of the radioactive isotope will be cut in half. (1/2)^(number of half-lives) = 3% number of half-lives = ln(0.03) / ln(0.5) This gives the number of half-lives as 5.06. Then 300 days = (5.06)(length of 1 half-life) length of 1 half-life = 300 / 5.06 = 59.29 days