the half life of a radioactive substance is one day. You have 100 grams. how much of the substance would be left after a week?
After t days, you have
100*(1/2)^t
To determine how much of the radioactive substance would be left after a week, we need to understand the concept of half-life.
The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay or change into another substance. In this case, the half-life is one day.
To calculate the amount remaining after a given time, we need to determine how many half-lives have passed and then calculate the remaining amount.
In one week, there are 7 days. Since the half-life of the substance is one day, we can calculate the number of half-lives that have passed by dividing the number of days by the half-life:
Number of half-lives = number of days / half-life
In this case: Number of half-lives = 7 days / 1 day = 7 half-lives
Now, to calculate the amount remaining, we use the formula:
Remaining amount = initial amount * (1/2)^(number of half-lives)
Given that we started with 100 grams, the calculation becomes:
Remaining amount = 100 * (1/2)^7
To simplify this calculation:
Remaining amount = 100 * 0.0078125
Therefore, after a week, there would be approximately 0.78125 grams (or 0.78 grams, rounded to two decimal places) of the radioactive substance remaining.