An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining after 18 minutes, to the nearest 10th of a grams
To find out how much of the element remains after 18 minutes, we need to use the formula for exponential decay:
N(t) = N(0) * e^(-kt)
where:
- N(t) is the amount remaining after time t
- N(0) is the initial amount
- e is Euler's number (approximately 2.71828)
- k is the decay constant (in this case, 26.8% = 0.268)
- t is the time in minutes
Given:
- N(0) = 820 grams
- k = 0.268
- t = 18 minutes
Plugging these values into the formula:
N(18) = 820 * e^(-0.268 * 18)
N(18) = 820 * e^(-4.824)
Calculating the value:
N(18) ≈ 820 * e^(-4.824)
N(18) ≈ 820 * 0.008934
N(18) ≈ 7.32068 grams
Therefore, to the nearest tenth of a gram, approximately 7.3 grams of the element remains after 18 minutes.