Carbon dating in exercise, you are given the ratio of carbon atoms in a fossil. use the information to estimate age of the fossil. in living organic material, the ratio of radioactive carbon isotopes to the total number of carbon atoms is about 1 to1012.(see example 2 in second 10.1) when organic materials 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
r = 10^-12(1/2)^t/5715 ,
where t is the time (in year) and t = 0 represent the time when the organic material died.
r = 0.22 * 10 - 12

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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70 years.

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