if you have an element that starts out at 40g and has a half-life of 10 days, you keep it for 30 days- how much doe you end up with?

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To determine the amount of the element remaining after 30 days, you need to understand the concept of half-life. The half-life is the time it takes for half of the substance to decay or transform into another element.

In this scenario, the element has a half-life of 10 days. This means that after 10 days, half of the original amount will decay, leaving only half the amount remaining. After another 10 days (20 days total), half of the remaining amount will decay again, resulting in a quarter (1/2 * 1/2 = 1/4) of the original amount remaining. After another 10 days (30 days total), the remaining amount will decay again, resulting in an eighth (1/2 * 1/2 * 1/2 = 1/8) of the original amount remaining.

To calculate the final amount, we can use the formula:

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

Where:
- Final amount is the amount after a certain time,
- Initial amount is the starting amount,
- Time is the duration for which you are calculating,
- Half-life is the time it takes for the substance to decay by half.

Plugging the values into the formula, we can calculate the final amount:

Final amount = 40g * (1/2)^(30 days / 10 days)

Simplifying the equation:

Final amount = 40g * (1/2)^3

Final amount = 40g * (1/8)

Final amount = 5g

Therefore, after 30 days, you would end up with 5 grams of the element remaining.