A particular substance decays in such a way that it loses one third of its weight each day if the substance originally weighs 300 grams, how much is left after 10 days

1 answer

If the substance loses one third of its weight each day, then after one day it would have $(1 - \frac{1}{3}) \times 300 = \frac{2}{3} \times 300 = 200$ grams. After the second day, it would have $\frac{2}{3} \times 200 = \frac{4}{3} \times 100 = \frac{400}{3}$ grams. After the third day, it would have $\frac{2}{3} \times \frac{400}{3} = \frac{800}{9}$ grams. And so on.

After 10 days, the weight of the substance would be $\frac{2}{3} \times \frac{800}{9} = \frac{1600}{27} \approx 59.26$ grams.

Therefore, after 10 days, there would be approximately 59.26 grams of the substance left.