Final answer:
To find the remaining mass of a decaying element after 15 minutes at a rate of 21.8% per minute, we use the formula for exponential decay, which involves the initial mass, the decay rate as a decimal, and time.
Step-by-step explanation:
A student has inquired about the amount of time it will take for an element with an initial mass of 670 grams to decay after 15 minutes, given that the element decays by 21.8% per minute. We can approach this problem using the concept of exponential decay. The formula to calculate the remaining mass after a certain time is:
M(t) = M_0 × (1 - r)^t
Where:
- M(t) is the mass remaining after time t
- M_0 is the initial mass
- r is the decay rate (expressed as a decimal)
- t is the time in minutes
Converting 21.8% into decimal form gives us 0.218. Now we can plug the values into the decay formula:
M(15) = 670 × (1 - 0.218)^{15}
Calculating this expression gives us the remaining mass after 15 minutes of decay.