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 gram?
To find the remaining mass after 18 minutes, we use the exponential decay formula:
A = P(1 - r)^t
where:
A = remaining mass after t minutes
P = initial mass
r = decay rate per minute (in decimal form)
t = time in minutes
In this case:
P = 820 grams
r = 0.268 (26.8% expressed as a decimal)
t = 18 minutes
Plugging in the values, we get:
A = 820(1 - 0.268)^18
A = 820(0.732)^18
A ≈ 820(0.00161)
A ≈ 1.3202 grams
Therefore, there is approximately 1.3 grams of the element remaining after 18 minutes.