Final answer:
To find the number of half-lives and the total time of decay, we can use the formula for exponential decay. By solving the equation, we find that 5 half-lives will have passed before the substance decays to 7.3 grams. The total time of decay is 5.21 minutes.
Step-by-step explanation:
To find the number of half-lives, we need to calculate the amount of substance that remains after each half-life. Let's use the formula:
Remaining amount = Initial amount * (1/2)^(number of half-lives)
Initially, the substance has 116.8 grams and we want to find the number of half-lives when it decays to 7.3 grams. Let's solve the equation:
7.3 = 116.8 * (1/2)^(number of half-lives)
Taking the logarithm of both sides, we get:
log(7.3) = log(116.8) + number of half-lives * log(1/2)
Using the properties of logarithms, we can solve for the number of half-lives. After calculating, we find that the number of half-lives is approximately 5.37. Since we can't have a fraction of a half-life, the answer is 5 half-lives.
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 1.042 minutes, and the number of half-lives is 5.
So the total time of decay is 1.042 minutes * 5 = 5.21 minutes.