If the sample has a half life of 5 seconds, how much is left after 25 seconds?

12.5%

25%

3.125%**

6.25%

25 s is 5 half-lives

(1/2)^5 = 1/32

looks correct

To calculate the amount left after a certain time, we can use the formula for exponential decay:

Amount remaining = (Initial amount) * (1/2)^(time / half-life)

In this case, the half-life is given as 5 seconds. So, after 5 seconds, half of the initial amount will remain.

Let's plug in the given values:

Amount remaining = (Initial amount) * (1/2)^(25 / 5)

Simplifying, we get:

Amount remaining = (Initial amount) * (1/2)^5

Now, we can calculate the amount remaining:

Amount remaining = (Initial amount) * (1/2)^5

Since the initial amount is not given, we cannot determine the exact amount remaining. However, we can determine the percentage of the initial amount remaining.

Let's calculate the percentage:

Percentage remaining = Amount remaining / Initial amount * 100%

Percentage remaining = [(Initial amount) * (1/2)^5] / (Initial amount) * 100%

The initial amount cancels out:

Percentage remaining = (1/2)^5 * 100%

Simplifying further:

Percentage remaining = (1/2)^(5) * 100%
Percentage remaining = 1/32 * 100%

Finally, we can calculate the exact percentage:

Percentage remaining = 3.125%

Therefore, the correct answer is 3.125%, as indicated by the option "3.125%" in the available choices.

The other choice was

1.5625%