Final answer:
After 16 minutes, the amount of an element that decays by 16.3% per minute can be calculated using the exponential decay formula. The initial mass is reduced by the decay rate raised to the power of time passed. final amount of the substance remaining after 16 minutes is 45
Step-by-step explanation:
To calculate how much of an element remains after it decays by 16.3% per minute for 16 minutes, we can use the formula for exponential decay: A = P(1 - r)^t, where A is the amount of substance left, P is the initial amount of substance, r is the rate of decay as a decimal, and t is the time in minutes.
Plugging the values into the formula, we get:
P = 780 grams (initial amount)
r = 16.3% or 0.163 as a decimal
t = 16 minutes
Therefore, A = 780(1 - 0.163)^16.
= 45.2586
= 45
the final amount of the substance remaining after 16 minutes. Round the result to the nearest 10th of a gram to provide the final answer.