A radioactive element has a half-life of 6.41 days. What percent of the original sample will be left after 15.0 days?

estimate: that is over 2 half lives, guessing 20 percent. The math

amountremaining=original*e^(-ln2*15/6.42)

decimal percent=e^(-ln2*15/6.42)=.199
or 19.9 percent

Thanks

To find the percent of the original sample that will be left after 15.0 days, we need to use the concept of half-life.

The half-life of a radioactive element is the amount of time it takes for half of the substance to decay. In this case, the half-life is 6.41 days, which means that after 6.41 days, half of the original sample will have decayed.

We can calculate the number of half-lives that have passed over the 15.0-day period by dividing 15.0 days by the half-life of 6.41 days:
Number of half-lives = 15.0 days / 6.41 days = 2.34 (approximately)

So, approximately 2.34 half-lives have passed in 15.0 days.

Now, to calculate the percent of the original sample that remains, we use the following formula:

Percent remaining = (1/2)^(number of half-lives) x 100

Plugging in the number of half-lives (2.34) into the formula, we get:

Percent remaining = (1/2)^(2.34) x 100 ≈ 29.8%

Therefore, approximately 29.8% of the original sample will be left after 15.0 days.