Final answer:
To determine the number of half-lives and the total time of decay, use the formula N = (log(Mt/M0)/log(1/2)), where N is the number of half-lives, Mt is the final amount, and M0 is the initial amount. Substituting the values, 4 half-lives will have passed before the substance decays to 8.3 grams, and the total time of decay is 8.18 minutes.
Step-by-step explanation:
To find the number of half-lives that have passed before the substance decays to 8.3 grams, we can use the formula N = (log(Mt/M0)/log(1/2)), where N is the number of half-lives, Mt is the final amount, and M0 is the initial amount. Substituting the given values, we get N = (log(8.3/132.8)/log(1/2)) = (log(0.0625)/log(1/2)) = (log(1/16)/log(1/2)). Using the change of base formula, log(1/16)/log(1/2) = (log(16)/log(2)) = 4. Therefore, 4 half-lives will have passed before the substance decays to 8.3 grams.
The total time of decay can be calculated by multiplying the half-life by the number of half-lives. In this case, the half-life is given as 2.045 minutes, and the number of half-lives is 4. So, the total time of decay is 2.045 minutes x 4 = 8.18 minutes.