assume the substance has a half-life of 11 years and the initial amount is 126 grams.
How much remains at the end of 8 years?
To find out how much remains at the end of 8 years, we need to use the half-life formula:
Amount Remaining = Initial Amount * (1/2)^(time / half-life)
In this case, the initial amount is given as 126 grams, the half-life is 11 years, and we want to find out the amount remaining after 8 years. Plugging these values into the formula:
Amount Remaining = 126 * (1/2)^(8 / 11)
To calculate this expression, let's break it down step by step:
1. Dividing 8 by 11: 8 / 11 = 0.7273
2. Calculating (1/2)^(0.7273): Raise 1/2 to the power of 0.7273 using a calculator.
(1/2)^(0.7273) ≈ 0.5899
Finally, multiply the result by the initial amount:
Amount Remaining = 126 * 0.5899
Amount Remaining ≈ 74.2166 grams
Therefore, at the end of 8 years, approximately 74.22 grams remain.