Final answer:
It will take 4 half-lives for the substance to decay from 118.4 grams to 7.4 grams.
Step-by-step explanation:
To determine the number of half-lives that will have passed before the substance decays to 7.4 grams, we need to calculate the number of half-lives it takes for the initial amount to decay to that level.
First, let's calculate the number of half-lives it takes for the initial amount of 118.4 grams to decay to 7.4 grams. Each half-life reduces the amount by half, so we need to divide 118.4 grams by 2.
118.4 grams ÷ 2 = 59.2 grams
Since 59.2 grams is still greater than 7.4 grams, we need to continue dividing by 2.
59.2 grams ÷ 2 = 29.6 grams
29.6 grams ÷ 2 = 14.8 grams
14.8 grams ÷ 2 = 7.4 grams
It took 4 half-lives for the initial amount of 118.4 grams to decay to 7.4 grams. Therefore, 4 half-lives will have passed before the substance decays to 7.4 grams.