The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance.
How many grams of the substance would be left after a week?
100 * (1/2)^7
5+46
Ah, radioactive substances, we sure know how to make things disappear, don't we? Well, let's put on our thinking caps and do some calculations, shall we?
After one day, half of the substance would have decayed. So, we'd be left with 100/2 = 50 grams.
After two days, half of that would decay, leaving us with 50/2 = 25 grams.
After three days, well, you guessed it, half of that would go "bye-bye," leaving us with 25/2 = 12.5 grams.
Now, if we keep going like this for a week, let me tap into my circus calculator...
After four days, we'd have 12.5/2 = 6.25 grams left.
After five days, it would be 6.25/2 = 3.125 grams.
After six days, we're down to 3.125/2 = 1.5625 grams.
Finally, after a whole week, we're left with 1.5625/2 = 0.78125 grams.
So, drumroll, please... after a week, we would have approximately 0.78125 grams of the substance left. And don't worry, it won't be causing any more radioactive mischief!
To determine how many grams of the substance would be left after a week, we need to calculate the number of half-lives that occur in a week.
Since the half-life of the substance is one day, there are 7 days in a week. Therefore, the number of half-lives in a week is equal to the number of days in a week.
After one half-life, half of the substance remains. So after one day, we would have 100 grams * 0.5 = 50 grams left.
After two half-lives (two days), another half of the remaining substance decays, leaving us with 50 grams * 0.5 = 25 grams.
Following this pattern, we can calculate the amount of substance left after each additional day:
- Day 3: 25 grams * 0.5 = 12.5 grams
- Day 4: 12.5 grams * 0.5 = 6.25 grams
- Day 5: 6.25 grams * 0.5 = 3.125 grams
- Day 6: 3.125 grams * 0.5 = 1.5625 grams
- Day 7: 1.5625 grams * 0.5 = 0.78125 grams
Therefore, after a week (7 days), approximately 0.78125 grams of the substance would be left.
To find out how many grams of the substance would be left after a week, we need to calculate the number of half-lives that occur in a week. Since the half-life is one day, there are seven days in a week, so we can calculate the number of half-lives as follows:
Number of half-lives = (Number of days) / (Half-life)
= 7 days / 1 day
= 7 half-lives
Now that we know the number of half-lives, we can calculate how much of the substance remains after that many half-lives. Each half-life halves the amount of substance, so after one half-life, we will have 50 grams left, and after two half-lives, we will have 25 grams left. We can continue this pattern:
After three half-lives: 50 grams / 2 = 25 grams
After four half-lives: 25 grams / 2 = 12.5 grams
After five half-lives: 12.5 grams / 2 = 6.25 grams
After six half-lives: 6.25 grams / 2 = 3.125 grams
After seven half-lives: 3.125 grams / 2 = 1.5625 grams
So, after a week, approximately 1.5625 grams of the substance would be left.