The amount of carbon-14 remaining in an organism, a, is equal to the product of the initial amount of carbon-14 in the organism, a0, and one-half to the power of n, where n is the number of half-lives the organism has experienced. if a frog initially contained 32 grams of carbon-14 and the half-life of carbon-14 is 5,730 years, how much carbon-14 remains in the frog after 17,190 years?

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.